Question

An experiment consists of boy-girl composition of families with 2 children.

(i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births ?

(ii) What is the sample space if we arc interested in the number of boys in a family?

Answer 1

Since a family has two children

(i) Then the sample space may be
$S=\left\{\right(B_1,B_2),(B_1,G_2),(G_1,B_2),(G_1,G_2\left)\right\}$
when subscript 1 and 2 represent elder and younger children.

(ii) Since the family has two children so, the following possibility of boys in the family

(a) No boys only girls
(b) One boy and one girl
(c) Two boys only
$\therefore$ S = {0, 1, 2}
S = {0, 1, 2}