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) $2 / 3$
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Answer:
Correct Answer: 54.(b)
Solution:
Formula:
- 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} $
BETA
