The probability of India winning a test match against south Africa 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
Select one:
O a. 1/4
b. 2/3
O C. 1/8
d. 1/2
Answers
Answered by
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Step-by-step explanation:
Let A
1
,A
2
and A
3
be the events of match winning in first, second and third matches respectively and whose probabilities are
P(A
1
)=P(A
2
)=P(A
3
)=
2
1
P(A
′
1
)=P(A
′
2
)=P(A
′
3
)=
2
1
∴ Required probability
=P(A
1
A
2
′
A
3
)+P(A
1
′
A
2
A
3
)
=P(A
1
)P(A
2
′
)P(A
3
)+P(A
1
′
)P(A
2
)P(A
3
)
=(
2
1
)
3
+(
2
1
)
3
=
8
1
+
8
1
=
8
2
=
4
1
a. 1/4 i
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