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Question: A, B, C in order cut a pack of cards replacing them after each cut, on the condition that the first ...

A, B, C in order cut a pack of cards replacing them after each cut, on the condition that the first who cuts a spade shall win the prize. Then the probability of B to win the prize is-

A

16/37

B

12/37

C

9/37

D

None of these

Answer

12/37

Explanation

Solution

Probability of cutting a spade = 1/4. A start the game.

P(2) = 3/4 . 1/4 + 3/4. 3/4. 3/4.3/4.1/4 +…. = 3/161−2764\frac { 3 / 16 } { 1 - \frac { 27 } { 64 } } = 1237\frac { 12 } { 37 }