Question by John C: How many children should a family plan to have so that the probability of having at least one child of each se?

How many children should a family plan to have so that the probability of
having at least one child of each sex is at least 0.95?




Best answer:

Answer by rauchers
1 - 0.5 ^(n-1) >=0.95

0.5^(n-1) >=0.05

ln 0.5^(n-1) >=ln 0.05

n-1 >= ln 0.05 / ln 0.5
n-1 >= 4.32
n> = 5.32
n=6

explaining
no mather what sex the first child has
the probability that secound child has the same sex is 0.5
and the probability th at 2nd and 3th child have the same sex is 0.5^2
so the probability that all n childs have the same sex is
0.5^(n-1)
to have at least one from other sex
1- 0.5^(n-1)
and it must be greater or equal to 0.95
1- 0.5^(n-1) >=0.95

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