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

• A. 1/8
• B. 1/4
• C. 1/2
• D. 2/3

Answer 1

Answer: (B)

Given, $P$ (India wins) $=1/2$
$\therefore P$ (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.
$\therefore$ Required probability $=P(LWW)+P(WLW)$
$=(\frac{1}{2}{)}^3+(\frac{1}{2}{)}^3=\frac{1}{4}$