Question

The probability of India winning a test match against Australia is \( \frac{1}{2} \), assuming independence from match to match. The probability that in a match series India’s second win occurs at third test match is

• A. \( \frac{1}{8} \)
• B. \( \frac{1}{4} \)
• C. \( \frac{1}{2} \)
• D. \( \frac{2}{3} \)

Hint:

In a series of independent events, the probability of a specific outcome is the product of individual probabilities.

Answer 1

The Correct Option is A

Step 1: Applying Probability Formula.
The event we are looking for is the occurrence of the second win in the third match, which means the first two tests should be losses and the third one should be a win. The probability of this event is: \[ P = \left( \frac{1}{2} \right)^3 = \frac{1}{8} \] Step 2: Conclusion.
The correct answer is (A), \( \frac{1}{8} \).