Probability Question 314
Question: The probability of India winning a test match against Westinies 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.
Options:
A) 2/3
B) 1/2
C) 1/4
D) 1/8
Show Answer
Answer:
Correct Answer: C
Solution:
Since, India’s second win occurs at the third test.
Therefore, the sample space is $ =[LWW,WLW] $ Where, L = losing the test W = winning the test.
$ \therefore $ P (India’s win occur at the 3rd test) $ =P(LWW)+P(WLW) $
$ =P(L)P(W)P(W)+P(W)P(L)P(W) $ (
$ \therefore $ Prob. From match to match is independent). $ =( \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2} )+( \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2} ) $ (Given) $ =\frac{1}{8}+\frac{1}{8}=\frac{2}{8}=\frac{1}{4} $
BETA
