Question

Probability of india winning match against Pakistan is 0.5 find the probability that india's 2nd win occur s in 3rd test in a 5 match series?

Answer 1

Probability of India winning match against Pakistan is 0.5 find the probability that India's 2nd win occurs in 3rd test in a 5 match series?

Solution

The probability of India winning a test match against Pakistan = $\frac{1}{2}$.

=> The probability of India losing a test match against Pakistan = $1 - \frac{1}{2} = \frac{1}{2}$.

The criteria here is "India's second win should occur at the third test".

The following table summarizes all the possibilities:

Out of all the 8 possibilities, the desired possibilities are two only (shown bold italic)

Probability that India's 2nd win occurs in 3rd test in a 5 match series $P = \frac{1}{8} + \frac{1}{8} = \frac{2}{8} = \frac{1}{4}$.

Answer: $\frac{1}{4}$.