One of Each

A couple decides to keep having children until they have at least one boy and at least one girl, and then stop. Assume each child is independently a boy or a girl with probability 1/2 each, and that there are no multiple births. What is the expected number of children the couple will have? Give an exact number.

• expected value
• optimal stopping

Source: Classic expected-value exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.