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.)

FMMFone M, three F'sFFFFMMMMFMFMFMFFtwo M's, two F'sthree M's, one FMFMFMFFFFMMMMFMMFFMFMMMFMMFFFFMMFFFMMMFMMFFM

Answer 1

Probability that a child is boy is 0.5 and that of girl is also 0.5

Thus, probability of a certain arrangement (permutation) to occur is

Events boy and girl are independent.

All arrangements are equally likely. So, clearly number of arrangements (events) should be 16.

The equally likely events are-

FFFF

MFFF    FMFF    FFMF    FFFM

MMFF FMMF FFMM MFFM    MFMF FMFM

FMMM    MFMM    MMFM MMMF

MMMM

These are all equally likely events foe the gender of 4 children.