Question

Suppose that each child born is equally likely to be a boy or a girl. Consider a family with exactly three children.

(a) List the eight elements in the sample space whose outcomes are all possible genders of the three children.

(b) Write each of the following events as a set and find its probability :

(i) The event that exactly one child is a girl.

(ii) The event that at least two children are girls

(iii) The event that no child is a girl

Answer 1

(a) All possible genders are expressed as :

S = {BBB, BBG, BGB, BGG, GBB,GBG, GGB, GGG}

(b) (i)Let A denote the event : ‘exactly one child is a girl’

A = {BBG, BGB, GBB}

(ii) Let B denote the event that at least two children are girls.

B = {GGB, GBG, BGG, GGG}, P (B) =4/8

(iii) Let C denote the event : ‘no child is a girl’.

C = {BBB}

∴ P (C) =1/8