Suppose that each child born is equally likely to be a boy or a girl.

1.	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» (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

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»

(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

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