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In a family with 5 children, what is the probability that a) there is at least one girl? b) there are exactly 2 girls?
1 Answer
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- Iggy RockoLv 72 weeks ago
a)
p(boy) = p(girl) = 1/2p(at least one girl) =1 - p(all boys) =1 - (1/2)^5 =
1 - 1/32 =
31/32
b)
p(two girls) =
5C2 * (1/2)^2 *(1 - 1/2)^3 =
5!/(2!(5 -2)!) * 1/4 * * 1/8 =
10 * 1/4 * 1/8 =
10/32 = 5/16
Alternatively,
p(two girls) =
# of combinations with 2 girls / # of all possible combinations =
5C2/2^5 =
(5!/(2!(5 - 2)!)) / 32 =
10 / 32 = 5/16
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