A family has 6 children. Assume that each child is as likely to be a boy as it is to be a girl. Find the
probability that the family has 6 girls if it is known the family has at least one girl.
P(all girls AND at least 1 girl) P(all girls)
P(all girls|at least 1 girl) = -------------------------------- = ------------------
P(at least 1 girl) P(at least 1 girl)
The oldest could be a boy or girl, that's 2 ways.
The next to oldest could be a boy or girl, that's 2 ways.
The 3rd to oldest could be a boy or girl, that's 2 ways.
The 3rd to youngest could be a boy or girl, that's 2 ways.
The next to youngest could be a boy or girl, that's 2 ways.
The youngest could be a boy or girl, that's 2 ways.
That's 2∙2∙2∙2∙2∙2 = 26 = 64 ways the 6 children could be.
P(all girls) = 1/64
P(at least 1 girl) = 1 - P(all boys) = 1 - 1/64 = 63/64
P(all girls) 1/64
P(all girls|at least 1 girl) = ------------------ = ------- = (1/64)(63/64) = 1/63
P(at least 1 girl) 63/64
Edwin
