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valkas [14]
3 years ago
14

A family decides to have children until it has three kids of the same gender. Assuming P(B) = P(G) = 0.5, what is the pmf of X =

number of children in the family?
Mathematics
1 answer:
olga nikolaevna [1]3 years ago
8 0
X takes values: { 3, 4, 5 }
where:  P ( X = 3 ) + P ( X = 4 ) + P ( X = 5 ) = 1
For X = 3 we have : BBB or GGG.
P ( X = 3 ) = ( 1/2 * 1/2 * 1/2 ) * 2 = 1/8 * 2 = 2 / 8 = 1/4
P ( X = 4 ) = ( 1/2 * 1/2 * 1/2 * 1/2 ) * 6 = 6 /16 = 3/8
P ( X = 5 ) = ( 1/2 * 1/2 * 1/2 * 1/2 * 1/2 ) * 12 = 12 / 32 = 3/8
1 / 4 + 3 / 8 + 3 / 8 = 8 / 8 = 1 

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