Pick your favorite example from chapter 2 and do the following:
1. Give an account of how an innumerate person might understand the situation.
2. Describe the math (statistics) that underlies the situation.
3. Explain why the use of numbers, math, and statistics would help a person understand the situation.
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Wednesday, March 4, 2009
Chapter 2
Posted by Mr. Wille at 2:07 PM
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39 comments:
Nada G.
I really like the example about the man who has a woman friend in the Bronx and a woman friend in Brooklyn, he is attached to both of them so doesn’t know if he should take the train to the Bronx or if he should take the train to Brooklyn so he decides that since each train runs every 20 minutes, he’ll just take the one that comes first. His Brooklyn friend starts complaining to him that he only comes to her ¼ of the time while his Bronx friend is sick of seeing him too much. Maybe, this man should figure out the problem but I guess he just doesn’t like thinking as like innumerate people. Well the statistics behind this is: the train this guy goes on depends on the schedule of it; for example: maybe the Bronx train comes at 7:00 and the Brooklyn train comes at 7:05, 20 minutes later the Bronx train comes at 7:20 and the Brooklyn train comes at 7:25, thus he ends up taking the Bronx train since that is the one that came first. Perhaps, this is what keeps on happening and that’s why one woman sees him ¼ of the time and the other sees him ¾ of the time. Innumerate people would probably have the same thinking as this man and not realize or even stop to think about what the real case is. Innumerate people have the characteristic of being lazy to think, thus they will fill in this situation because all it requires is thinking. If the man thought about the timing of each train he would have probably been able to see each woman half of the time. Therefore, the statistics are very important in this case.
Keith M.
My favorite example from chapter 2 is the stock market scam. First an 'adviser' sends 32,000 letters to potential investors in a stock index. The letter gloats his expertise and in 16,000 letters he will predict the index will rise and the other 16,000 he will predict the index will fall. No matter what happens to the index, the 'adviser' will only continue to sent letters to those who received a 'correct' prediction. Of those 16,000 he will send half one prediction and the other half the other prediction. This goes on until 500 people get 6 'correct' predictions in a row. He encourages those 500 people to send $500 to him for the seventh 'correct' prediction. An innumerate person would be completely blown away at the adviser's predictions and would almost immediately send $500 to the con. That would be a (500 x 500)= 250,000 payout for the con. Using a big number like 32,000 allows a person to predict one guess to half of those people and predict the other guess for the other half. Going along this pattern allows a person to do this multiple times until he has a considerable amount of people willing to part with money for more valuable information. (1/2) to the 6th power, which is also (1/2)x(1/2)x(1/2)x(1/2)x(1/2)x(1/2) equals to about 0.015625 (1.5 percent). But this times the number of people he conned (32,000) equals to exactly 500, which is the amount of people who paid the con. Simple multiplication could help prevent the seemingly complicated actions performed by a con artist.
Candy L.
My favorite example is the stock market scam also. It's amazing how it's done. Imagine if a stock market advisor sent you correct prediction for 6 times in a row, and he/she ask you to sent $500 to him/her for next week's stock investigation, I bet everyone will do it, why not? He/She had correct predition all the time right? The truth is this: The "adviser" send out 32000 letters to stock investigators, half of the letters he/she sent out indicates that the stock next week will rise, and the other 16000 states that the stock next week will fall. So no matter the stock rises or falls, the "advisor" have sent out 16000 letters with the correct prediction. Then he/she just have to do the same thing for 6 weeks. He/She had sent to 500 people the correct prediction for 6 weeks! This is why be a "numerate person" is so important, and again I realize how "innumerate" I was before I read this book, I'll sure believe the "advisor" if I'm a stock investigator.
Jeffrey L. -
I enjoyed reading the example about the man who travels alot. It said that he was concerned about a bomb being on a plane. He then finds the probability of a bomb being on a plane and figures out that it is low. He felt that it was not low enough for him so now he travels with a bomb in his own suitcase. He then continues on to say that the probability of two bombs being on the plane is even lower. This shows me his innumeracy because although it is true that the probability of 2 bombs on a plane is smaller than the probability of 1 bomb, he guarantees that there will be at least 1 bomb on the plane. When he brings the bomb on the plane, the chance of a bomb on a plane gets increased drastically because he is bringing a bomb himself. This means that the probability of a bomb on the plane is 100%. This shows his innumeracy because then the probability of 2 bombs on the plane is the same as 1 bomb on the plane since he is always travelling with a bomb. If he knew that one of the bombs was always 100% on the plane, he would understand that the probability is exactly the same. This just goes to show you how innumerate people can misunderstand a situation.
Rondelle B.
My favorite example from chapter two was the first one of the guy who was concerned about the bomb being on his plane. This guy wants the probability of having a bomb on his plane to be almost impossible. The probability that he came up was probably somewhere around 15%. Therefore, he brings his own bomb so the probability of having two bombs on the plane would be less than the probability of having one bomb. So I guess the percentage number is the only thing he considers in his choice. The use of numbers wouldn't really help him, it would just be commonsense because he just raised the probability of having one bomb on the plane to 100%.
Shomir U.
My favorite example from chapter two is as follows:In 1964 in Los Angeles a blond woman with a ponytail snatched a purse from another woman.The thief fled on foot but was later spotted entering a yellow car driven by a black man with a beard and a mustache Eventually two people fit to this description
were found but no hard evidence linked these people to the crime.The prosecutor argued that the probability of someone meeting the given criteria is 1/12,000,000, a number so low that the couple found must be the criminal.The case
was presented to the Californian supreme court. The defense attorney in that trial argued that 1/12,000,000 is relevantly probable with California's 2,000,000 couples, which is equal to 8%. This probability was not small and that another couple existed with such characteristics. An innumerate person would have thought that couple to be the criminals due to the fact that the two people meeting these characteristics is 1/12,000,000, which is very unlikely. They, like the prosecutor(who didn't considered the couples population in Los Angeles, might have been doing his job or innumerate to a certain degree, wouldn't have taken into consideration how many couples their are in Los Angeles. The use of numbers helps a person understand how probable a couple with yellow car,man with mustache,woman with blond hair,woman with ponytail,black man with beard, and interracial couple in a car.This compared to the couple population in Los Angeles will tell us if we can be certain these people are guilty are if another couple exists. Even though a lot of other factors still exist like specifically where the crime occurred and how long has it been since it occurred that compared to how far the couples were from the crime scene to give us a sense of whether or not these people could have committed a crime. In a case like this characteristic probabilities occurring helps understand much.
P.S. Scooby Doo could solve this crime.
MY favorite example of the book is when the man brings a bomb on to the plane becausehe believes the probability of having two bombs on the plane is impossible. An inummerate person might get this wrong because the man doesn't realize that these variables are independent, that is him having a bomb on the plane has no affect on the other person having a bomb on the plane. He found out that the possibilty of having a bomb on his plane is small, but apparently not small enough for him, so he walks now with a bomb. HE figures that two bombs being on the same plane is infinitesmal.
Sibely A.
I was skeptical of the motive behind John Allen Paulos' decision to write this book before I came to read chapter two. Right at the beginning of the chapter, he gives examples of what a person might consider a coincidence, and shoots them down by calling them innumerate because they’ve underestimated the frequency of these so called coincidences. It’s kind of ridiculous to think of every little thing that seems remotely related to another thing as a coincidence, but apparently the innumerate will assume this almost right away. Some examples of this that he gave was of a person saying, “Oh, my brother-in-law went to school there, too, and my friend’s son cuts the principal’s lawn, and my neighbor’s daughter knows a girl who was once a cheerleader for the school.” The innumerate would be surprised at these relations because it seems almost impossible that so many people could be connected to this one school, but the chances are actually pretty high that one person knows another person, who happens to know another person, who you happen to know. Then he adds a more humorous example of this underestimation of frequencies: The Reagan-Gorbachev INF treaty was signed on December 8, 1987, exactly seven years after John Lennon was killed. This may seem like a coincidence, but there are only 365 days a year, so there’s a 1 in 365 chance that John Lennon would die on the same date as the signing of the treaty. It’s a really interesting thing, isn’t it? To live knowing that there are no true coincidences, and that the probability of something we think is really rare to occur is really not quite as impossible as we once thought it was. What a world! I guess we’re all really innumerate on the inside. It’s inevitable. John Allen Paulos makes us really rethink all that we knew.
Damaris F.
Wow, I agree with the many people before me.
My favorite example from chapter two also happens to be about the man who carries a bomb around with him when he travels in an airplane. It's sort of a mathematical joke in a way.
An immumerate person might understand the situation as this: The man is one of those people who are freaked out about the chance of traveling in a plane that may possibly carry a bomb. So he founds out the probability of a bomb being on a plane, which is low because of all the security on planes nowawdays. But he decides there is still a chance, and he wants to get it as close to 0% as possible, for a better chance of surviving the trip. So now he carries a bomb with him every time he travels- and he travels a lot. He decides that the probability of TWO bombs being on a plane is nearly impossible.
I guess I can depict the statistics behind this to be for example, (made up) (1/15) x (1/15) = 1/30. Since the numerator are all the same, and 30 is a bigger denominator, this means that there is less chance of TWO bombs being on the same flight at the same time. Of course, this sort of is reasonable.
However, since he carries a bomb with him, he automatically raises the chance of a bomb flying with him to be 100%. And even if another person takes a bomb with them too or not won't make much of a difference.
So in my opinion, yes his answer is reasonable. A chance of TWO bombs being on the same plane is "infinitesmal." But it doesn't really count if he's the one bringing one of the bombs. That just brings the probabilty down to as if it was one bomb, because his bomb is a sure thing. So he's not really innumerate. ((But why would he take a bomb with him on a plane?? He's not innumerate, just really weird...))
My favorite example is the story of the man on the Johnny Carson Show. He was describing the probability of two people sharing the same birthday, and how the probability is 50% if there are at least 23 people in the group given. Johnny, being skeptical, attempts to disprove him by proving that of the 120 people watching his show, none of them were born on March 19. In fact, Johnny Carson is the perfect example of the innumerate: he takes a concept, true or not, and grossly misinterprets it in order to disprove it. In reality, the theory states the probability that at least two people will have the same birthday, and does not state that it has to be any particular day. The number of how many people are necessary for at least two people to have been born on any specific day is much larger.
-Louis L.
Tony L.
My favorite example in the chapter was when a man who was afriad of acts of terroism on an airplane calculated the odds of someone planting a bomb on the plane. even though it was a low chance that there will be a bomb on the plane he still didn't think it was low enough. Therefore he bought a bomb on to the plane as well thinking that another person that might have a bomb on the plane too was extreamly extreamly low. If you think of what the pseson did, it will make sense even if it seems ridiculously ridiculous. The point of the man's new "travel item" is to lower the chance of another one having a bomb on the plane. If the Chances of a terroist having a bomb on the plane is 30%...the traveller brings a bomb so that the chances of having two bombs on the same plane will be lowered to an exteamly low possibility. Almost to nothing. An innumerate pseron might think the chances of the bombs on the plane will increase because he/she wouldnt understand probablility.Instead the possibility of two bombs on a plane become 0% it would become 100% for a innumerate person.The understanding of probability is fundamental for the understanding of statistics.
Roberto B.
My favorite example is the one about the blond lady with the pony tail who stole the purse and then entered a car driven by a bearded, mustachioed black man. Then they found a blond women with a ponytail who frequently talked with a black man with a beard and 'stash.Then they when to court bla bla bla. The prosecutor then says that there is a 1/12,000,000 change of that couple existing. To this point I agree with him because he used realistic information and the chances look slime for this couple. Then when they appeal they had a prosecutor say that there more than one couple with the given characteristics. I do not agree with this because that other couple probably lives in Wyoming and they did not do anything. Anyways that gave the court enough doubt to release them. I think that the enumerate person here is the jury because they where fooled by suck a weak statistic disprove thing.
Benjamin G.
My favorite example in this chapter was the man who carried a bomb around with him every time he traveled, as he didn't think the probability of somebody carrying a bomb onto the plane was small enough for the amount he traveled. An innumerate person (such as the man himself) would think that, since the chance of one person carrying the bomb onto the plane is so small, that the chance of two being on the same plane would be even smaller. This is not the case, however, as these are two independent variables, which mean that they have no effect on each other; if the original man has a bomb, it does not change the chance of somebody else on the plane also having a bomb, just because he is carrying one. The chance of somebody having a bomb on an airplane is extremely small. If somebody brings a bomb onto a plane, it does not affect the chance of me bringing a book onto a plane, because they are completely different objects and have no relation to each other. The exact same thing could be said about me bringing a different bomb onto the plane. Just because one person doesn't have a bomb, it doesn't mean that I have less of a chance of bringing a bomb onto the plane.
In chapter two Paulos talks about probability and coincidence. I like this chapter more, because I am one person that likes to say "what a coincidence". Now I know its not all about coincidence. My favorite example is in chance encounters. Two strangers sat next to each other on a plane and found out that the wife of one was in a tennis camp run by an acquaintance of the other's. These types of things ar commmon, because each of the 200 million adults in the U.S. knows about 1,500 other people. There is a probability that one in a hundred would have an acquaintance in common. Also more than 99 in a hundred will be linked by two other people. Two people chosen at random will probably be linked in some way. An innumerate person would not understand this, because you can't imagine that through out your life you have known so many people and that in one way or another you are all linked by each other. If a person is celebrity or well known the number of intermediates or people linking you them is smaller. If you knew Michelle Obama, N would represent the number of intermediates between you. Then N+1 would represent the number of intermediates from you and Barack Obama. The use of statistics would help someone understand a situation, because you would really no what would more likely or less likely happen and make smart decisions according to that.
Clara S.
My favorite example from Chapter 2 is the story about the man who constantly travels and develops a fear of there being a bomb on his plane, so he packs one every time he goes somewhere. At first, I was innumerate, myself. I thought he was a lunatic to bring a bomb onto his own plane. After I read on, I realized that, even though the chance of there being a bomb on a plane was small, it was still there. The man mathematically proved that the probability of there being two bombs on one plane was an infinitely small number. At first glance, this man looks completely crazy, but with the aid of math, specifically probability, one realizes it's actually quite an intelligent idea.
Amanda Z.
In Innumeracy, one example I found quite amusing was Paulos’ story about a man who was afraid of the possibility of a bomb on board his plane. Although the man realizes that the chances of a bomb on being on the plane were unlikely, the probability was still too high for his comfort. Therefore, the man began carrying a bomb in his briefcase since the chances of there being two bombs on board a plane was immensely small- infinitesimal. One can see that the chances of a particular flight carrying two people who have bombs in their luggage are very much smaller because if the probability that there’s one person is 1/n, then the probability that there are two people would be 1/n^2. Although his reasoning is so far correct, he fails to understand that in this case it is the probability of B happening given that A has already happened. If the two events A and B are independent then the probability of B given A is the same probability as P(B), because by definition if they’re independent one happening shouldn’t affect the other. Due to that fact that in this man’s case, his carrying a bomb is a independent event from another person carrying a bomb, his carrying a bomb does nothing to change the probability of the existence of another bomb on the plane.
Th example that struck me most was the man with two girlfriends. One lived in the Bronx and one lived in Brooklyn. To make the decision of which girlfriend to see, he takes whichever train comes first. He ends up seeing one girl 1/4 of the time and the other 3/4 of the time. The mistake is obvious, but the man seemed baffled. It is very likely that the two different trains have different schedules. If the man waits for whichever train comes first, thae man will take that train for the majority of the time, and see that girl more often.
Christian J.
In the second chapter in the book Innumeracy, one example I found to be very interesting was that everybody is linked by at most 6 people. So anybody can contact anyone through only 6 people. Even though this completely destroys the theory of coinsidences but it is mathematically proven, thus destroying destiny. The author John Allen Paulos determines that each person knows about 1,500 people in their lifetime. Heres how he mathematically proves that all people are linked somehow: "let N equal the amount of people between you and President Regan, so the equation for Elvis Presely would be (N+1) because Regan knew Elvis".
BrooksR
Casinos have been popular even since their conception largely because, in a way, they deceive gamblers into believing that the likeliness of profiting from gambling is very high. Unless someone is truly numerate, they will easily overlook the facts and continue to gamble with the fallacy that their high stakes are justified by high probabilities of winning. They could be told that the probability is very low, but it is still likely that they would not believe it because they do not fully understand probability and how it works. For instance, the game: "chuch-a-luck is a very enticing game to those who do not understand how small their chances of winning really are. In this game, the player selects any number from 1 to 6 on a regular dice. Then, the operator will roll three sets of dice and will award the player $3 if the number chosen lands on 3 die, 2$ if the number lands on 2, and 1$ if it lands on 1 of the dice. In addition, if the number chosen lands on none of the dice, the player must pay the operator 1$. To the innumerate, this game is very enticing; however when the counting principle is used to compute the probability of winning $3, it is evident that the actually probability of winning 3$ out of one trial is (1/6 * 1/6 * 1/6) or 1/216, which is a very low probability. In theory, a person could lose 215 trials before getting any reward. The highest reward is 3$ so the highest a person would theoretically get from 216 trials is -$213. In fact, the odds of losing a trials is 125/216, which is more than half to the time. However, to the innumerate, who does no know these odds, this game still happens to be very enticing.
Nina A.
My favorite part of chapter 2 of innumeracy
is the bit where John Allen Paulos talks about randomness with X and O situations. He said "The following is a computer printout of a random sequences of X's and O's, each with the probability of a half."
Then there is random x's and O's. He says that since there are little patterns and such in the scenario that it is easier to believe that it is random then if it was all X's and then all O's or just XOXOXOXOXOXOXOXOXOXOXOXOXOXOXOXO the whole way.
An innumerate person might think that this is false and that the little patterns and such in the scenario of X's and O's make it more likely not to be random and that the XOXOXOXOXOXO would seam more random to them.
The math in this situation is saying that that in a true random situation where one for example a one toss will have no effect on the one after it and has nothing to do with the one before it. So in a random scenario it is the same amount of probability to have XXXXXXXXXXXXXXXXXXXX and OOOXXOXOXOXOOOOOXXXO.
The use of numbers math and statistics would help a person (even an innumerate person) because it gives people almost visuals in there head and really walks them through it to help the person understand best.
Favorite example in chapter two of the book is the first example that was given with the bomb. The man was too worried that when ever he goes on the plane there would be a possibility of a bomb being on board. However the truth of the matter is that the possibility of a bomb ever being on the plane was very very slim. in fact it would probably never happen when this passenger is one the plane. Now the passenger decides that the probability is two low, so he brings in a second bomb. what he doesn't realize is that the he just decreased the overall chance of a second bomb being on board.
in this example it is important to understand that the passenger was not aware that by bringing a bomb on the plane does not increase the chance of someone else bringen a bomb with out any outside variables. what he has done was the exact opposite of what he was looking for, he has decreased the chance almost infiniely. in this story the passenger is the innumerate person who does not fully understand the power of statistics
Trevor L.
My favorite example of people being innumerate in Innumeracy was the Stock Market Scam. One person could say they have credentials and send 6 free statements that gave his predictions of the stocks. In the example, a person could convince 32000 people to give him their address to send the statements to them. He would send 32000 statements, 16000 predicting the stocks go up and 16000 predicting the stocks go down. After that, the people who recieved a correct statement would get more statements. 8000 ups and 8000 downs. After doing this 6 times, there are 500 people who recieved 6 straight correct predictions. This person can charge $500 for the 7th prediction and $500 from 500 people is $250,000.
Now, an innumerate person would see this and think that he must be smart. But everyone knows nobody is perfect and nobody can make that many predictions on the mark. A numerate person would especially know because the chance that someone would get 6 straight stock predictions correct in a free trade economy is next to none unless they had inside information. A smart person would do a background check as well, but thats another story.
Grissel G.
The example in Chapter 2 that was most appealing to me was the example at the beginning of the chapter. It was of a pilot that had a great fear that one day there would be a bomb aboard his plane. In order to solve this problem, he brought a bomb of his own onto the plane, and the reasoning behind this was that the odds of there being two bombs at the same time would be “infinitesimal.” Anyone can pick up on the innumeracy in this so-called “solution”. To explain it in mathematical terms, the odds of a bomb being on a plane can be represented as 1 flight out of N flights, or 1/N. Two bombs on a single flight would be 1/N*1/N, or (1/N) ². If N were 500,000, then the odds of having two bombs on a single flight would be (1/500,000) ², or 1/25,000,000,000. This is true if both bombs were independent cases, however, the bomb deliberately places on the plane was not independent, so there is only one independent, making the odds of both bombs being on the plane 1/500,000 again.
I asked my sister this question; if she would bring her own bomb on a plane so the odds of someone else bringing their own bomb would be almost impossible. She looked at me, laughed a bit, and then said, “That makes no sense. You’re only making the odds of having a bomb on a plane 2/500,000.”
My favorite example, as some people, is the example with the man and the bomb. In this example, a man who frequently travels on planes is worried about the chance that he will get on a plane with a bomb in it. However, once he found the percentage, he started carrying around a bomb in his own bag, because the probability of two bombs on a single plane is almost inconceivable. This man was clearly innumerate, because only an innumerate person would not consider the fact that if this man continues to carry around a bomb in his bag, the chances that a bomb is on the plane he is riding in is 100%, because of the bomb in his own bag. This will not change whether or not another person will also bring a bomb onto the plane his/herself. So the chances of someone bringing a bomb onto a plane has not changed simply because the man has a bomb in his bag too. No matter what the probability of a man/woman bringing their own bomb onto a plane is, the fact that this man himself has this bomb in his own bag means that you are taking the probablility that someone will bring a bomb onto a plane and multiplying it 1 (100%).
Aleksandar P
My favorite example in Chapter 2 is the Stock market scam. The way it works is that a con man sends out 32000 giving predictions to people whether their index will rise or fall. There is a 50% chance or being right, so letters are sent out to 16000 people giving predictions. This goes on for 6 rounds until there are 500 people left, and they are required to pay $500 dollars to get their next prediction. The con artist probably sends out letters to 32000 so he can get enough people to pay. since 500/32000 is about 1.56%, that means that the people who did get all 6 predictions were very lucky. If these people who are innumerate had a better understanding of math, they would have noticed the trick quickly. They would have seen that the letters are just 50% predictions, and that if they made it to the 6th prediction, that they were just lucky. They would see that paying $500 to receive more info would be a scam since all the info given thus far was pure luck.
im going to talk about the bomb statistic. A person carries around a bomb because he is afraid of the plane having a bomb and since he carries one and someone else has one, the chance ot 2 bombs beingon a plane is smaller than the chance of there being one bomb. the probabilit of one bomb being on the plane is high so the person is more scared. But once this person starts carrying a bomb, two bombs on the same plane has less f a chance of happening.
im going to talk about the bomb statistic. A person carries around a bomb because he is afraid of the plane having a bomb and since he carries one and someone else has one, the chance ot 2 bombs beingon a plane is smaller than the chance of there being one bomb. the probabilit of one bomb being on the plane is high so the person is more scared. But once this person starts carrying a bomb, two bombs on the same plane has less f a chance of happening.
-sadichchha a.
Sergio G.
My favorite example would be that of the Man in New York who has a friend in Brooklyn and one in the Bronx, and is equally attached (unattached?)to both of these women, could care less about which train he should get on for a date.
His Brooklyn friend, who has feelings for him, complains about his showing up only 1/4 of the time for their dates, while his Bronx friend is tired of him, and complains about having to see him on all of 3/4 of their dates.
This is due to the way the trains are scheduled, one passing by his station every 20 minutes. It goes like this: A Bronx train passes at 7:00, then a Brooklyn train passes at 7:05, followed by a Bronx train on 7:20, which is followed by a Brooklyn train at 7:25.
The man probably takes the Brooklyn train more often because he prefers to take the train that will come sooner than the last, because that may cause him to assume it's faster, the Brooklyn train. So 3/4 of the time he prefers to take a presumably fast train. The 1/4 of the time in which he chooses the Bronx train is when he doesn't feel rushed at all, or prefers to look around, should the hypothetical Bronx-bound train go above ground.
Craig H.
My favorite example in Innumeracy is the stock market scam. A stock market advisor sends out 32,000 letters with 1/2 claiming that the stock market will go up and the claiming it will go down, because the stock market goes either up or down a half of the letters predictions will be correct. He repeats this with correct half until it dwindles down to 500 people who had six correct predictions in a row. He then ask for a $500 fee for more 'valuable' predictions. To the innumerate person receiving this letter he or she probably thinks that if they were six times in a row how can they be wrong about this one. However, that person is blind to the fact that initially 16,000 people received incorrect predictions, or that she is just one 500 out of 32,000. If that person were to use probability that person would realize the chance of the prediction being correct again will always remain 50%, and will avoid being scammed.
Kelly Y.
My favorite example from chapter 2 would be the one with number of intermediates between people. An innumerate person would just think it as a coincident or wouldn't notice how we can be link to other people in a chain, even to people that is really famous. People are all linked somehow either by the huge or small number of intermediates between them. The number of intermediates would be smaller if the person is celebrity because they know a lot more people. Let say the number of intermediates between person A and you are be n and between you and person B would be n+1 because person A knows person B. So it really matters who you make friends with because if you meet the right person, they might lead you to the right path and is a friend of someone famous.
In chapter two Paulos writes about probability and coincidence in life. My favorite example from the chapter is in the “Chance Encounters” section on page 38-40. The example basically describes how unknowingly almost everyone has something in common through a common contact. “If we assume each of the approximately 200 million adults in the United States knows about 1,500 people, and that these 1,500 people are reasonably spread out around the country, then the probability is about one in a hundred that they will have an acquaintance in common, and more than ninety-nine in a hundred that they will be linked by a chain of two intermediates.” An innumerate person would have a hard time believing this claim. In his or her mind there are so many people in the country alone that there is no way that there is such a high percentile in knowing a common friend with almost everyone. At first I was confused but after relating it to something more consistent with my life help me understand. Its is like Facebook or Myspace and the amount of people you have in your “people you may know” that you have never seen but they have something in common with you. However with a person that is innumerate it still would not be enough. The way to explain this simplicity is through numbers which are universally the same. The intermediate is the amount of people you know between someone. With celebrities it is quite easy to explain since they have met many people. N is the number of intermediates between me and David Archuleta. Then the number of intermediates between me and Paula Abdul is less than or equal to (N+1) since David knows Paula. Next with Simon there are no more than (N+2) since David knows Paula who knows Simon. It is a quite remarkable how through such a small chain one can be connected to so many people.
-monika c.
Bix the W.
Chapter two of Innumeracy is about the existence (or non-existence) of coincidence and how it is really probability at work. In this chapter, John Allen Paulos gives an example of how probability works; A man goes on the Johnny Carson show and tries to explain to Johhny Carson that to have a fifty percent chance of finding two people who share a birthday, one only needs twenty three people. Johnny Carson does not believe the man and asks his studio audience of 120 people whether any of them share his birthday of March 19th. They say no. An innumerate person, like the man who told this to Johnny Carson, would either be very confused or think that this disproves it. It does not. The fact is that there will be a 50 percent chance of 2 people sharing ANY birthday among 23 people, not a particular birthday
Joey B.
My favorite example from chapter 2 of innumeracy was when the man with the briefcase always boards with a bomb in his briefcase because he figured that the probablility of there being two bombs on a plane was less than there only being one. This particularly explains his innumeracy because if he was that 1 chosen person that got the bomb on his plane, it wouldnt matter if he had the briefcase or not. He also could've gotten caught (or might've actually gone to jail for it). He thought that his having a bomb would affect the probability as one of the factors, but it did not.
I loved the part where Johnny Carson show came up and he tried to tell Mr. Carson that to have a one in two chance to find someone who has the same birthday, you only need to collect 23 random people. So, the host goes ahead and asks people in the audience if they have the mans birthday and they all say no. The man was very disappointed and felt wrong because of his unfortune but coming to this conclusion would be like saying that a coin comes out heads every single time. This man jumped to conclusions because of his overwhelming innumeracy and his belief that he was proved wrong by luck and chance.
--- Christopher B.
Emily S.
Like many people that also posted a blog, I liked the example about the connections between people. I've heard this termonology before, six degrees of seperation and what not. I actually asked an innumerate person, my brother, what he thought about that. he said that there was no way he was connected to someone like Tyra Banks or Jessica Alba. I tried to explain that if you know someone that knows someone that knows Jessica's ex, then it would be that number plus one. He still didnt get it though.
John-Corey M.
In this chapter my favorite example was the one about how all people in the US are connect by 3 people. this reminds me of the idea of six degrees of seperation how everyone in the world is connected by 6 people. An innumerae person would not understand this or even comprehend this. Also i liked the one about the attractive girl and how she would meet people and may not pick any of them. and the unatractive would meet her 3rd choice first and 1st choice 2nd. An innumerate person would she how it is possible for numbers to know this
My favorite example from Chapter two of Innumeracy is the stock market scam. An Innumerate person will understand it because its simple. Since there are only two ways a stock can go, up or down, all the scammer has to do is predict a decline for half the people and a rise for the other. The half that succeed would use it again and all the scammer has to do is repeat the process. The number mainly is 1/2^n n being how many times the scam has been done. The people who have succeeded n times will end up paying a fortune to the scammer where the chances are always in his/her favor.
My favorite example from chapter two was the bithday one where people get all excited about birthdays being on the same day as another person. An innumerate person would think that it's a rare and cool thing because out of the 366 days in the year(a leap year)there would need to be 367 people in order for 2 perple to share the same birthdate. This makes them innumerate because only a numerate person would know that it would only take 23 people to share the same bithdate. THe use of numbers would help an innumerate person know the right things and not make a complete fool out of themselves the next time they know someone who has the same birthday as them.
Munesh S.
Evan Y.
The part of chapter I most was the part where a man always carries a bomb onto an airplane to avoid being in a terrorist attack. His reasoning is that he saw the odds of a bomb being taken aboard an airplane. He saw that the odds were small but he wanted to be sure. So he carries a bomb onto the airplane in his suitcase because he thinks the odds of there being two bombs in the same airplane is even smaller. However he does not understand that his taking a bomb onto an airplane does not affect the chances of somebody else also bringing one. If he had understood math better he may have realized this and not brought the bomb onto the airplane.
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