This is a probability question:
A couple plans to have 3 children. find the probability that they couple has at least one child of each sex. ten points to best answer
A couple plans to have 3 children. find the probability that they couple has at least one child of each sex. ten points to best answer
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Let A represent the event of having at least one child of each sex.
(Assuming the couple does not have the 3 children simultaneously.....)
P(A) = n(A)/n(S)
n(S) = 2^3 = 8 (this number represents the number of ways that the children may be born; the number of subsets using permutations)
n(A) = n(S) - 2 (the 2 comes from having all boys and having all girls; the rest of the subsets must have at least one girl and one boy)
P(A) = n(A)/n(S) = 6/8 = 3/4
Therefore, the probability that the couple has at least one child of each sex is 3/4 or 75%.
(Assuming the couple does not have the 3 children simultaneously.....)
P(A) = n(A)/n(S)
n(S) = 2^3 = 8 (this number represents the number of ways that the children may be born; the number of subsets using permutations)
n(A) = n(S) - 2 (the 2 comes from having all boys and having all girls; the rest of the subsets must have at least one girl and one boy)
P(A) = n(A)/n(S) = 6/8 = 3/4
Therefore, the probability that the couple has at least one child of each sex is 3/4 or 75%.