$2$ 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.
$2$ 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.
Let us denote $2$ boys and $2$ girls in room $X$ as $B_{1}, \,B_{2}$ and $G_{1},$ and $G_{2}$ respectively. Let us denote $1$ boy and $3$ girls in room $Y$ as $B_{3},$ and $G_{3},\, G_{4}, \,G_{5}$ respectively.
Accordingly, the required sample space is given by
$S =\{X B_{1}, \,X B_{2},\, X G_{1},\, X G_{2}$, $Y B_{3},\, Y G_{3},\, Y G_{4}$, $Y G_{5}\}$
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