A probability problem by Anthony Pham
Kenny, Jack, and Sarah are playing a game of Old Maid using a standard deck of cards. In this game, the Old Maid is a random card that was removed. Kenny discarded a pair of A's, 2's, 4's, 7's, and Q's. Jack discarded 2 pairs of 5's and K's, and a pair of 8's and J's. Sarah discarded a pair of A's 6's, 9's, 10's, and Q's.
What is the face value of the Old Maid?
The answer is 3.
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1 solution
Moderator note:
Good observation about the parity of the cards.
There are four cards to a rank (A, 2, 3,...J, Q and K) except for the rank of the card withheld as the Old Maid. When the 51 cards are distributed to three persons, at least a pair of each rank is discarded by a person, except for the Old Maid, since it has only three cards and it may or may not be discarded as a pair. We note that all the ranks are discarded as pair except for 3 , therefore, 3 is the Old Maid.