Question

Describe the sample space for the indicated experiment :
$2$ boys and $2$ girls are in Room $X$, and $1$ boy and $3$ girls in Room $Y$.
Specify the sample space for the experiment in which a room is selected and then a person.

Answer 1

Given:
$2$ boys and $2$ girls are in Room $X$,and $1$ boy and $3$ girls in Room $Y$. A room is selected and then a person

Room $X:$
Let $B_1,B_2$ and $G_1,G_2$ are the boys and girls in room $X$ respectively.
Possible outcomes are when room $X$ is selected then a person: $\{X{B}_1,X{B}_2,X{G}_1,X{G}_2\}$

Room $Y:$
Let $B_3$, and $G_3,G_4,G_5$ are the boys and girls in room $Y$ respectively.
Possible outcomes when room $Y$ is selected then a person : $\{Y{B}_3,Y{G}_3,Y{G}_4,Y{G}_5\}$

Hence the required sample space is
$S=\{X{B}_1,X{B}_2,X{G}_1,X{G}_2,Y{B}_3,Y{G}_3,Y{G}_4,Y{G}_5\}$.