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:
Solution:
(a) 1/8
(b) 1/4 (c) 1/2
(d) 2/3
Solution follows here:
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
Answer (b)
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