Chapter 4 Risk: Thrill-seeking genes take us for a ride
Taking risks is costly but fun. Have you heard about the new state lottery game? It’s called, "Take a dollar and throw it in the trash." Actually, that’s not quite fair. State lotteries return about 50% of the amount wagered, so the game is more aptly called "Take fifty cents and throw it in the trash."
Why do we derive pleasure from making terrible bets? Part of the explanation is that we are terrible mathematicians. We can’t seem to calculate odds correctly. Take the big drawing in the California state lottery, for example, where a bet consists of picking six numbers between 1 and 51. To win, these six numbers must match, in any order, the six randomly drawn numbers. Given these rules, what is the chance of winning? Write down an approximate answer.
Here’s another brainteaser. Chinese families place a high value on sons, yet the Chinese government exerts extreme pressure to limit family size. Let’s assume that the chance of having a girl is exactly 50%, but every couple stops having babies once they have a son. So half of the families have just a single boy, a quarter of the families have one boy and one girl, an eighth have one boy and two girls, etc. In this scenario, what percentage of Chinese babies will be male? (The answer is below.)
One more. Imagine that you are a doctor and one of your patients asks to take an HIV test. You assure her that the test is unnecessary as only one woman out of a thousand with her age and sexual history is infected. She insists, and sadly the test result indicates viral infection. If the HIV test is 95% accurate, what is the chance that your patient is actually sick?
Here are the answers. Let’s start with the HIV test. When doctors and staff at Harvard Medical School were asked this question, the most common answer was a 95% chance that the patient was sick. They missed the mark by a mile ...