- #1

BenVitale

- 72

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And, Column By John Allen Paulos

__Scenario 1__: A woman has two children, the older of whom is a boy. Given this knowledge, what is the probability that she has two boys?No problem here, the answer is 1/2

__Scenario 2__: Assume that you know that a woman has two children, at least one of whom is a boy. You know nothing about this boy except his sex. Given this knowledge, what is the probability that she has two boys?We have come to accept that the probability the woman has two boys is 1/3, not 1/2.

Here's the kicker:

Suppose that when children are born in a certain large city, the season of their birth, whether spring, summer, fall, or winter, is noted prominently on their birth certificate. The question is: Assume you know that a lifetime resident of the city has two children, at least one of whom is a boy born in summer. Given this knowledge, what is the probability she has two boys?

Suppose that when children are born in a certain large city, the season of their birth, whether spring, summer, fall, or winter, is noted prominently on their birth certificate. The question is: Assume you know that a lifetime resident of the city has two children, at least one of whom is a boy born in summer. Given this knowledge, what is the probability she has two boys?

This appears to be essentially the same as the

__scenario 2__. But instead, they would find that 7/15 of these women have two boys.

An increase in probability from 1/3 to 7/15 !

Doesn't this change in probability seem strange?

I got a bit confused after reading the following problem:

**I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?**

Answer: the probability of two boys is 13/27

Source: http://alexbellos.com/?p=725