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. 44569
• B. 44565
• C. 44563
• D. 44595

Answer 1

Answer: (B)

44565

Answer 2

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)
\hspace30mm =\bigg(\frac{1}{2}\bigg)^3 +\bigg(\frac{1}{2}\bigg)^3=\frac{1}{4}