QUESTION

# 2 boys and 2 girls are in room X and 1 boy and 3 girls are in the room Y. Specify the sample space for the experiment in which a room is selected and then a person.

Hint: A sample space is a collection or a set of possible outcomes of a random experiment.The samples spaces for a random experiment is written within curly braces ‘{ }’

Let us denote 2 boys and 2 girls in a room X as ${b_1},{b_2}$ and ${g_1},{g_2}$ respectively.

Also, let us denote 1 boy and 3 girls in a room Y as ${b_3}$ and ${g_3},{g_4},{g_5}$ respectively.

Now, the sample space which we get in that room is chosen first.

Suppose we choose room X, then we will choose boys and girls of room X only.

And if we choose room Y we will choose boys and girls of room Y only.

So the sample space will be { $X{{b_1},X{b_2},X{g_1},X{g_2},Y{b_3},Y{g_3},Y{g_4},Y{g_5}}$ }

NOTE: In these types of questions if we choose room X then we will choose boys and girls of room X only and if we choose room Y then we choose boys and girls of room Y only.