Probability of India winning a test match against West Indies is frac{1}{2} . Assuming independence

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14.Probability

hard

The probability of India winning a test match against West Indies is $\frac{1}{2}$. Assuming independence from match to match, the probability that in a $5$ match series India's second win occurs at the third test, is

A

$\frac{2}{3}$

B

$\frac{1}{2}$

C

$\frac{1}{4}$

D

$\frac{1}{8}$

(IIT-1995)

Solution

(c) The sample space is $[LWW,\,\,WLW]$

$\therefore \,\,\,P(LWW) + P(WLW)$

= Probability that in $5$ match series, it is India’s second win

$ = P(L)P(W)P(W) + P(W)P(L)P(W)$

$ = \frac{1}{8} + \frac{1}{8} = \frac{2}{8} = \frac{1}{4}.$

Standard 11

Mathematics

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