## Thursday, 10 November 2011

### Probability-9 (IIT-1995)

The probability of India winning a test match against West Indies is ½. 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) 1/8          (b) 1/4        (c) 1/2              (d) 2/3
Solution follows here:
Solution:
The probability of India winning a test match against West Indies = ½
=> The probability of India loosing a test match against West Indies =1- ½ = ½
The criteria here is “India’s second win should occur at the third test”
The following table summarizes all the possibilities:
 1st Match 2nd Match 3rd Match P(E) = P(E1)*P(E2)*P(E3) India loosing all of the first three L L L 1/2*1/2*1/2 = 1/8 India winning one of the first three W L L 1/2*1/2*1/2 = 1/8 L W L 1/2*1/2*1/2 = 1/8 L L W 1/2*1/2*1/2 = 1/8 India winning two of the first three L W W 1/2*1/2*1/2 = 1/8 W L W 1/2*1/2*1/2 = 1/8 W W L 1/2*1/2*1/2 = 1/8 India winning all of the first three W W W 1/2*1/2*1/2 = 1/8

Out of all the 8 possibilities, the desired possibilities are two only (shown in green colour)
Probability     =1/8 + 1/8
= 2/8 = 1/4