Question

$2$ 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:

The two rooms are $X$ and $Y$.

In room $X-2$ boys, $2$ girls

$[B_1,B_2,G_1,G_2]$

In room $Y-1$ boy, $3$ girls

$[B_3,G_3,G_4,G_5]$

Case1:

When room $X$ is selected, there are four probabilities of members solution

$\{x{B}_1,x{B}_2,x{G}_1,x{G}_2\}$

Case 2:

When room $Y$ is selected, there are four probabilities of members solution.

$\{y{B}_3,y{G}_3,y{G}_4,y{G}_5\}$

Therefore, Sample space

$S=\{x{B}_1,x{B}_2,x{G}_1,x{G}_2,y{B}_3,y{G}_3,y{G}_4,y{G}_5\}$