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# The Tuesday Birthday Problem

#### Anonymous Coward writes | more than 4 years ago

1

An anonymous reader writes "I have two children, one of whom is a boy born on a Tuesday. What's the probability that my other child is a boy?

Believe it or not, the Tuesday thing is relevant. Well, sort of. It's ambiguous. Read the article to find out the answer.

In honor of Martin Gardner."

### exactly 1 in 2 (1)

#### Spazmania (174582) | more than 4 years ago | (#32724408)

Because your boy born on Tuesday is a constant in the problem, not a variable. The only variable is the gender and weekday for your other child.

If you rephrase the question: "In families with two children at least one of which is a boy born on Tuesday, what's the probability the other is a boy?" then the answer is 13 in 27.

There are 2 genders x 7 days x 2 genders x 7 days = 196 equally likely gender/day of week combinations for families with two children. I then eliminate 169 of the 196 possibilities with the criteria that one must be a boy born on Tuesday.

That non-random elimination biases the problem - I eliminate cases including 156 boys and 182 girls. The remaining 27 cases must thus include 40 boys and 14 girls. Since all 27 cases must have one boy that leaves 13 boys and 14 girls as possibilities for the other child.

I also eliminated families with some number of children other than 2 but that elimination doesn't bias the problem since exactly the same number of girls and boys are eliminated.

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