Question

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. (Let M represent a boy (male) and F represent a girl (female). Select all that apply.) MMFF, FFFF, MMMF, two M's two F's, MFFF, FMMM, FFMF, FMFF, three M's one F, FFFM, MFFM, MFMF, one M three F's, FMFM, FMMF, MMFM, MMMM, FFMM, MFMM

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

Answer 1

Answer:

a) Total 16 possibilities

MMMM

FFFF

MMMF

MMFM

MFMM

FMMM

FFFM

FFMF

FMFF

MFFF

MMFF

MFMF

MFFM

FFMM

FMMF

FMFM

b) P(MMMM) = 1/16