Caroline, Joan and Sam all go shopping. They all buy a present, and all of the presents are the same size and wrapped in the same paper. At the check-out the parcels get mixed up. What is the probability that……
1) At least one of the three women gets the present she bought?
2) Only one woman gets a wrong present?
If you have not tried to solve it, have a go now. For everyone else the answer is after the break.
Let’s assume that the presents A, B and C belong to Caroline, Joan and Sam. There are then 6 ways of distributing the presents:
Caroline, Joan, Sam
1: A B C
2: A C B
3: B A C
4: B C A
5: C A B
6: C B A
Only in cases 4 and 5 does no one get the right present. As such, there are 4 out of 6 scenarios in which someone gets the right present, and so the chances are two thirds.
2) The probability is zero. If only one woman gets the wrong present then the other two get the right present, and so the situation simply can’t happen.
Did you solve it? Any other solutions?
I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.