If a committee has 7 members? Find the probability of having more female members than the male members given that the probability of having a male or female member is equal
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in a committe of 7 members probability of having more female members than the male members = 1/2
Step-by-step explanation:
a committee has 7 members
n = 7
probability of having a male or female member is equal
P (F) = P(M) = 1/2
probability of having more female members than the male members
= Probability of 4 Female + 5 Female + 6 Female + 7 Female
= ⁷C₄(1/2)⁴(1/2)³ + ⁷C₅(1/2)⁵(1/2)² + ⁷C₆(1/2)⁶(1/2)¹ + ⁷C₇(1/2)⁷(1/2)⁰
= 35 (1/2)⁷ + 21(1/2)⁷ + 7(1/2)⁷ + 1(1/2)⁷
= (35 + 21 + 7 + 1)(1/2)⁷
= 64 (1/2)⁷
= 64/128
= 1/2
probability of having more female members than the male members = 1/2
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