easy Probability

Baby Boy

A release-checked easy problem for training Conditional Probability.

Question

A hospital nursery has $3$ baby boys and an unknown number of baby girls. A mother just gave birth to a child of unknown gender and it is added to the nursery. The doctor then picks up a random child in the nursery and it is a baby boy. Assuming that births of boys and girls are equally likely, find the probability that the mother just gave birth to a boy.

Practice focus

This Probability problem is tagged Conditional Probability. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.