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Book Review: Innumeracy

I just finished Innumeracy.  It was good, not great.  The subject is timeless, and so all the timely references kind of threw me off.  There were too many references to Thatcher and Reagan, for example.  It never got too technical, but when I did want to dig deeper, the internet was at the ready.  Some parts of note, with search terms you can use to read that bit from Amazon's Search Inside feature:

Optimal Strategy for Finding A Life Partner
(search for Myrtle in the book.)

First, figure about how many serious relationships you're likely to have, if you never settled on one.  (Are you conservative, or a floozy?)  Then, pass up the first 37% of your suitors.  After that, stop with the best-so-far.  Mathematical proof included.

Should You Be Concerned If You Test Positive?
(search for depressed in the book.)

Assume there is a test for cancer which is 98 percent accurate, and that one out of 200 people (.5%) actually have cancer.  You test positive!  Do you freak?

Imagine that 10,000 tests are administered.  Of these, 50 will have cancer (.5%), but only 49 test positive because the test is only 98% accurate.  Of the 9,950 cancerless people, 2% will erroneously test positive for a total of 199.   Thus, there are 248 positive tests, of which only 49 are true.  So the probability of actually having cancer after testing positive is only 49/248 or about 20%!

Payout of Interrupted Gambling Game
(search for Pascal in the book.)

Two men bet on a series of coin flips.  The first to win any six flips will win $100.  The game, however, is interrupted after only eight flips, with the score at 5 to 3.  How should the pot be divided?

A.  The man with 5 wins should get the $100.
B.  The man with 5 should get 5/8 of the pot, and the man with 3 should get 3/8 of the pot.

Since the probability that the man with 5 wins would have won is 7/8 (the only way the second man could win is by winning 3 flips in a row, a feat with probability of 1/8 = 1/2 * 1/2 * 1/2), the man with 5 wins should get 7/8 of the pot, and the other man only 1/8.

Relevance of Abuse in O.J. Simpson's Trial
(search for Simpson in the book.)

Alan Dershowitz argues that since fewer than one in a thousand men who batter their wives or girlfriends go on to murder them, the court should not have allowed testimony that Simpson battered his wife.  Paulos writes, "The statement is true but astonishingly irrelevant since it fails to take into account the obvious fact that there was a murder victim.  Using Bayes' theorem and some widely available crime statistics, one can conclude that if a man batters his wife or girlfriend and she later turns up dead, the batterer is the murderer more than 80 percent of the time, and this without any individuating circumstances or further evidence."

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