Consider a family with 3 children. Assume the probability that one child is a bo

Question

Consider a family with 3 children. Assume the probability that one child is a boy is 0.5 and the probability that one child is a girl is also 0.5, and that the events “boy” and “girl” are independent.

(a) List the equally likely events for the gender of the 3 children, from oldest to youngest.

(b) What is the probability that all 3 children are male? Notice that the complement of the event “all three children are male” is “at least one of the children is female.” Use this information to compute the probability that at least one child is female.

Explanation / Answer

a)

MMM

MMF

MFF

FFF

FMM

FFM

FMF

MFM

b) P( all 3 are male) = ?

=1-P(atleast 1 is female)

= 1- 7 cases/8 cases

=1 - 7/8 = 1/8

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