The Room X: {B1, B2, G1, G2}
Room Y: {B1, G1, G2, G3}
Sample space: {RXB1, RXB2, RXG1, RXG2, RYB1, RYG1, RYG2, RYG3}.
In the given scenario, where there are two rooms, Room X and Room Y, each containing a different combination of boys and girls.
we can construct a comprehensive sample space to represent all possible outcomes when selecting a room and then a person within that room.
The sample space, denoted as S, encompasses the various combinations of room and individual selections.
For Room X, housing 2 boys (B1, B2) and 2 girls (G1, G2), the sample space includes the following possibilities: RXB1, RXB2, RXG1, and RXG2.
On the other hand, Room Y, with 1 boy (B1) and 3 girls (G1, G2, G3), contributes additional outcomes: RYB1, RYG1, RYG2, and RYG3.
Each outcome in the sample space signifies a distinct event, where the first part indicates the selected room, and the second part identifies the chosen person within that room.
This comprehensive sample space encapsulates all potential results, offering a clear representation of the experiment's various permutations and combinations as a room is first chosen, followed by the selection of an individual within that room.