Probability Ques 54

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 $5$ match series India’s second win occurs at third test, is

(1995, 2M)

(a) $1 / 8$

(b) $1 / 4$

(c) $1 / 2$

(d) $2 / 3$

Show Answer

Answer:

Correct Answer: 54.(b)

Solution:

Formula:

Definition of Probability :

  1. Given, $P$ (India wins) $=1 / 2$

$\therefore \quad P$ (India losses) $=1 / 2$

Out of $5$ matches India’s second win occurs at third test.

$\Rightarrow$ India wins third test and simultaneously it has won one match from first two and lost the other.

$\therefore \quad$ Required probability $=P(L W W)+P(W L W)$

$ =(\frac{1}{2})^{3}+(\frac{1}{2})^{3}=\frac{1}{4} $



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