A newly married couple decides to continue having children until they have one of each sex. If the events of having a boy and a girl are independent and equiprobable, how many children should this couple expect?

Two, one of each ;)

Three.

The probability for exactly two children is 1/2 (i.e, the chance of the sex of child 2 being different from child 1). The probability of 3 children is (1/2)^2; the probabiliy of four is (1/2)^3 etc. So the expected value is:


\frac 2 2 + \frac 3 4 + \frac 4 8 + \frac 5 {16} + ...
=\displaystyle\sum _{i=1} ^ {\infty} \frac {i+1} {2^i} = 3.