## February 21, 2016

### Birth Probability Puzzle

James and Catherine are a married couple. They have two children, one of the child is a boy. Assume that the probability of each gender is 1/2.
What is the probability that the other child is also a boy?

Jerry Critter said...

The probability is the same as the first time. It is like a coin toss. History plays no role. The probability is 1/2. If we did not know that the first child is a boy, the probability of having two boys would be 1/4.

Josh D. said...

They have two children. The probabilities are:
P(BB) = 1/4
P(BG) = 1/4
P(GB) = 1/4
P(GG) = 1/4

One of the children is a boy, so we can eliminate the GG option. This leaves us with the first three scenarios still as viable options. Of the three options remaining, only 1 of the 3 options is BB. Thus, the probability is 1/3.

Saying "one of the children is a boy" is different than the case where they said something like "The older child is a boy." In that case it would be 1/2, not 1/3.

larry atkinson said...

1/2. Mutually exclusive events.

Josh D. said...

A thorough description is here: