Originally Posted by AssumeTheCrown

This problem is a classic case of conditional probability. The average person has trouble understanding it. The boy/girl problem can be tested by repeatedly tossing 2 coins and recording the results(say 20 times). There are 3 possible outcomes ( 4 really) - HH,HT,TT.
Now we ask what is the probability of the other coin being a TAIL given that one of them is a HEAD? Straight away we can ignore all the TT's from our sample (cross them off the list) because the question asks "given that one of them is a head". That will leave only HH's and HT's in the list. Now put a circle around any T in the list. You should find about a 2:1 ratio or a 2/3 to 1/3 Tails to Heads.

This better illustrates conditional probability. With the coin or the boy/girl examples there are 4 possible outcomes - HH, HT, TH, TT each with a 25% chance of occuring. When we ask the question "given that one of them is a ..." we are effictively saying that one of these situations did not happen. In the above example we eliminated TT leaving HT, TH, HH. Now we are left with 2 T's and 1 H with the corresponding H which we were told existed. So the probability of the other coin being a T is 2/3 and an H is 1/3.