Question

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. \( \frac{1}{6} \)

Hint:

For probability questions involving a sequence of events, use binomial probability and the independence of events to calculate the desired probability.

Answer 1

The Correct Option is C

Step 1: Use binomial probability.
We need the probability that the second win occurs at the third test. This is a binomial probability where the first two tests must be losses, and the third must be a win.
Step 2: Conclusion.
The probability of this event is \( \frac{1}{4} \). Final Answer: \[ \boxed{\frac{1}{4}} \]