Question

There are two children in a family. If it is known that at least one child is a boy, find the  that both children are boys.

Hint:

Use conditional probability: \( P(A|B) = \frac{P(A \cap B)}{P(B)} \).

Answer 1

Possible outcomes for two children (B = Boy, G = Girl): \[ \{BB, BG, GB, GG\} \] Given that at least one child is a boy, the sample space reduces to: \[ \{BB, BG, GB\}. \] The 64abecb1454319c1ac04f9e6 of both being boys: \[ P(BB | \text{at least one boy}) = \frac{P(BB)}{P(BB, BG, GB)} = \frac{1}{3}. \]