The probability of India winning a test match against Australia is (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:

Question

The probability of India winning a test match against Australia is (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) (1/2) (B) (1/3) (C) (1/4) (D) (1/5)

Tardigrade Admin · Accepted Answer

Required probability = (Prob. of winning a test in the first two matches) . (prob. of winning a test in third match) = 2C1 ((1/2))2-1 ((1/2))1. ((1/2)) = (2!/1!) . (1/2). (1/2). (1/2) = (1/4)

Q. 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 5 match series India's second win occurs at the third test is:

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{1}{4}$

$\frac{1}{5}$

Required probability = (Prob. of winning a test in the first two matches) . (prob. of winning a test in third match)
$=^{2} C_{1} (\frac{1}{2})^{2 - 1} (\frac{1}{2})^{1} . (\frac{1}{2}) = \frac{2 !}{1 !} . \frac{1}{2} . \frac{1}{2} . \frac{1}{2} = \frac{1}{4}$

Q. The probability of India winning a test match against Australia is 21​. Assuming independence from match to match the probability that in a 5 match series India's second win occurs at the third test is:

21​

31​

41​

51​