Question

The probability of India winning a test match against South Africa is 1/2 assuming independence form match to match played. The probability that in a match series India's second win occurs at the third day is ______.

Options

• `1/8`

• `1/2`

• `1/4`

• `2/3`

Answer 1

The probability of India winning a test match against South Africa is 1/2 assuming independence form match to match played. The probability that in a match series India's second win occurs at the third day is `underlinebb(1/4)`.

Explanation:

Given, probability of winning a test match, P(W) = `1/2`

Probability of losing a match, P(L) = `1 - 1/2 = 1/2`

Probability that India's second win occurs at the third day

= P(L) . P(W) . P(W) + P(W) . P(L) . P(W)

= `1/2 . 1/2 . 1/2 + 1/2 . 1/2 . 1/2`

= `1/8 + 1/8`

= `1/4`