Conditional Probability: Boys and Girls 2
Your new colleague, Ms. Parker, is known to have two children. If you see her walking with one of her children and that child is a boy, what is the probability that both children are boys?
Answer
Given that you have observed one child as a boy, the possible combinations for her two children reduce to:
Assuming equal likelihood for a child to be boy or girl, the probability that both children are boys is:
Notes and comments
Comment 1: This scenario differs from the "at least one boy" problem because here you know specifically which child is a boy. In the "at least one boy" case, the outcomes could be Boy-Boy, Boy-Girl, or Girl-Boy, but once you see a particular child who is a boy, the ordering is fixed (the observed child is the boy), leaving only Boy-Boy and Boy-Girl as possibilities. Hence, the probability calculation simplifies to \( \frac{1}{2} \).