Indian Institute of Foreign Trade 2016 Solved Paper

Question : 15 of 123

Marks: +1, -0

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

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