There are two boxes. Box I contains one white card and two black cards and Box II contains one white card and a black card. Two persons P and Q play a game. P picks a card randomly from Box I. If P finds the white card, P wins and the game stops. If P finds the black card, Q draws a card randomly from Box II. If Q finds the white card, Q wins. The game stops whether Q draws the white card or the black card. Which one of the following is correct?
- AIf P loses, Q wins
- BIf Q loses, P wins
- CBoth P and Q may win
- DBoth P and Q may lose
Explanation
P wins outright with probability 1/3 (white from Box I). If P draws black (2/3), Q draws from Box II (one white, one black): Q wins with 1/2 and loses with 1/2. The outcome 'P loses (black) and Q loses (black)' has probability 2/3 x 1/2 = 1/3, so both P and Q may lose. They cannot both win (P's win ends the game), (A) fails because Q may also lose after P loses, and (B) fails because Q only plays after P has lost.