Probability 3 Question 16
16. 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) $2 / 3$
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Solution:
- 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 $=P(L W W)+P(W L W)$
$$ =\frac{1}{2}^{3}+\frac{1}{2}^{3}=\frac{1}{4} $$
