The Hot Hand and the Clutch Hitter

Regardless of how rare an event may seem to be, the probabilities are quite predictable. When playing sports it is probable that the player accuracy would be 50%. He says that me more you make attempt the more of a pattern you will see in you results. The fewer attempts that you make will barely show a pattern because your attempt would be constant. Because of the differences in sports, people can be “lucky” and have spurts. That spurt is the Hot hand in basketball and the clutch hitter in baseball. Paulos admires theses streaks but he also says that is possible to be accurate but not probable.

Expected Values

If one examines the laws of probability, one can see that there is bound to be a "streak" if enough tries were tried. The key is, it seems to be calling attention to the positive outcome of the situation while ignoring the unsuccessful outcome. Those positive outcomes are the expected values. One expects for the out come to be good when test. Paulos uses the example of Blood testing and your expected value is probability of the blood being healthy rather than being diseased. He uses another example of gambling in a Casino and the expected value is the number on the dice that the person picks. He says that it is 1 out of 6 times that you would get that expected value. He also mentions that if you have more attempts it raises your probability.

Some Birthday vs. a Particular Birthday

Paulos uses the assumption that each of the United States’ adults knows about 725 people spread throughout the U.S., there is a 1 in 100 probability that two people will have an acquaintance in common. There is more than a 99 out of 100 chance that the strangers will be linked by two intermediates. Paulos backs up this theory by those of shared birthdays. He says that one mistake many people make is to look for a specific event opposed to a particular event when trying to prove the theory. For example, it may be highly unlikely that two people in a location share the birthday of March 16, yet it is very likely that two people in a crowd will have a birthday in common. “Some birthday” is any days within a specific month, but the “Particular Birthday” is the day in the specific month.

Fair Coins and Life's Chance of Winners and Losers

Fair Coins and Life’s Chance of Winners and Losers
In "Fair Coins and Life's Chance of Winners and Losers" Paulos explained that when comparing coins there is a fifty percent chance of either getting a tail or a head. However, if one begins an experiment of flipping a coin a hundred times, the outcome may not always come out to be fifty to fifty. One may flip the coin and receive an outcome of ninety-two heads to eight tails. In concluding, this means that our outcome in an experiment will not always be fifty percent.

A Stock Market Scam

A Stock Market Scam

In A Stock Market Scam John Allen Paulos explains how people focus on the good and filter out the bad. He starts off by explaining that because stalk market advisors tend to use complex language, it's really easy to scam people and make a profit. He elaborates on how a stock market advisor makes two contradictory predictions to two different groups of potential investors. He focuses on the group with the correct "prediction" and further divides that group to repeat the process until five hundred people have received six consecutive correct "predictions". If they wish to get the seventh prediction they must pay five hundred dollars, resulting in 250,000 dollar profit. This will cause a fad and people will follow along. Another example he uses for filtering out the bad and emphasizing on the good is when he talks about casinos. When someone wins at a casino tons of lights go off and everyone sees but when someone loses there is no recognition. He also mentions how the radio, TV, and film have caused people to no longer be satisfied with their "local celebrities." All in all, this deliberate or subconscious act of filtering out the bad and focusing on the good creates the optimum environment for scams to thrive.

Coincidence and Law

Paulos applies probability to the law, using a case from Los Angeles in 1964 as his basis of proof. The scenario is a blonde woman with a ponytail snatched a purse from another woman. The thief fled and escaped into a yellow car driven by a black man with a mustache. Police found a couple who matched the description and convicted them despite lacking hard evidence to link the couple to the crime. With the facts of the case agreed upon by all parties, the prosecutor used probability to achieve a guilty verdict. The chances of each fact occurring are as follows: yellow car 1/10, man with mustache 1/4, woman with ponytail 1/10, blonde woman 1/3, black man with beard 1/10, interracial couple in car 1/1,000. By multiplying the fractions, the probability of all the conditions being met is 1/12,000,000. Therefore, the couple in question must be guilty since the odds of another couple meeting the criteria is so low.

Choosing a Spouse

One of the more humorous cases Paulos approaches mathematically is choosing a spouse. To introduce the concept, Paulos writes “There are two approaches to love-- through the heart and through the head. Neither one seems work very well alone, but together... they still don’t work too well.” Although I’d seriously doubt the validity of any relationship advice from Mr. Paulos, he focuses on whether to settle down or try to find a better option. Suppose an eligible bachelor or bachelorette will meet N marriage candidates in their romantic life. In most cases, the best spouse is not in the first 37% of candidates. One should then reject the first 37% and then marry the first ‘heartthrob’ (or perfect spouse) after the initial 37%. This formula only works because the man or woman in question ranks her suitors numerically. In real life, however, interest declines over time and a partner’s strengths and weaknesses cannot be boiled down to one number.