The probability of India winning a test match against West-Indies is 1 / 2 assuming independence from match to match. The probability that in a match series India's second win occurs at the third test is :

Question

The probability of India winning a test match against West-Indies is 1 / 2 assuming independence from match to match. The probability that in a match series India's second win occurs at the third test is : (A) (1/8) (B) (1/4) (C) (1/2) (D) (2/3)

Tardigrade Admin · Accepted Answer

Required probability =P(A1 A2 prime A3)+P(A1 prime A2 A3) =P(A1) P(A2') P(A3)+P(A1 prime) P(A2) P(A3) =((1/2))3+((1/2))3=(1/8)+(1/8)=(1/4)

Q. The probability of India winning a test match against West-Indies is 1 / 2 assuming independence from match to match. The probability that in a match series India's second win occurs at the third test is :

$\frac{1}{8}$

$\frac{1}{4}$

$\frac{1}{2}$

$\frac{2}{3}$

Required probability
$= P (A_{1} A_{2}^{'} A_{3}) + P (A_{1}^{'} A_{2} A_{3})$
$= P (A_{1}) P (A_{2}^{'})$ $P (A_{3}) + P (A_{1}^{'}) P (A_{2}) P (A_{3})$
$= (\frac{1}{2})^{3} + (\frac{1}{2})^{3} = \frac{1}{8} + \frac{1}{8} = \frac{1}{4}$