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Indian Institute of Foreign Trade 2016 Solved Paper
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© examsnet.com
Question : 15
Total: 123
The student mess committee of a reputed Engineering College has n members. Let P be the event that the Committee has students of both sexes and let Q be the event that there is at most one female student in the Committee. Assuming that each committee member has probability 0.5 of being female, the value of n for which the events A and B are independent is
2
3
4
None of the above
Validate
Solution:
(b)
P
(
P
)
=
1
−
1
2
n
(when all males)
−
1
2
n
(when all females)
P
(
Q
)
=
1
2
n
(when all males)
+
n
×
1
2
×
1
2
n
−
1
(when one female and rest males)
P(P
∩
Q) = exactly one female
=
n
×
1
2
×
1
2
n
−
1
For independent events
P(P
∩
Q) = P(P) × P(Q)
n
2
n
=
(
1
−
1
2
n
−
1
2
n
)
(
1
2
n
+
n
2
n
)
Solving we get n = 3
© examsnet.com
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