First slide

Theorems of probability

Question

Three persons A, B, C in order cut a pack of cards replacing them after each cut. The person who first cuts a spade shall win a prize. The ratio of the probabilities of their winning is

Easy

A

16:12:9
B

12:16:9
C

9:12:16
D

4:3:2

Solution

$P (A) = p + q^{3} p + ....... = \frac{16}{37}$
$P (B) = \frac{12}{37}$

$P (A) : P (B) : P (C) = 16 : 12 : 9$

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