In each of the following, 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.

Let X denote the event Room X is selected, Y denote the event Room Y is selected

B1,B2 denote the event a boy is selected from room X ,B3 denote the event a boy is selected from Room Y and G1,G2 denote the event a girl is selected from Room X andG3,G4,G5 denote the event a girl is selected among the three girls from Room Y

The problem is solved by dividing into two cases

Case 1: Room X is selected

We define the possible outcomes by an ordered set (x , y)

x denotes the event Room X is chosen

y denotes the second event a student is selected

Sample Space S₁={(X,B1),(X,B2),(X,G1),(X,G2)}

Case 2: Room Y is selected

We define the possible outcomes by an ordered set (x , y)

x denotes the event Room Y is chosen

y denotes the second event a student is selected

Sample Space S₂={(Y,B3),(Y,G3),(Y,G4),(Y,G5)}

The overall sample space

S={(X,B1),(X,B2),(X,G1),(X,G2),(Y,B3),(Y,G3),(Y,G4),(Y,G5)}