Consider a family with 4 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 4 children, from oldest to youngest. (LetMrepresent a boy (male) andFrepresent a girl (female). Select all that apply.)

MMFF

FFFF

FMFM

FFFM

MFFF

MFMM

FFMM

MMFM

two M's, two F's

FMMF

FMFF

one M, three F's

MMMF

MFFM

MMMM

FFMF

MFMF

FMMM

three M's, one F

(b) What is the probability that all 4 children are male? (Enter your answer as a fraction.)

Notice that the complement of the event "all four 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. (Enter your answer as a fraction.)