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dembajang · Sep 1, 2010, 08:11 AM

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?

Curlyben · Sep 1, 2010, 08:12 AM

Two, one of each ;)

ebaines · Sep 1, 2010, 09:25 AM

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:

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