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.

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Solution

Let us denote 2 boys and 2 girls in room X as B₁, B₂ and G₁, G₂ respectively. Let us denote 1 boy and 3 girls in room Y as B₃, and G₃, G₄, G₅respectively.

Accordingly, the required sample space is given by S = {XB₁, XB₂, XG₁, XG₂, YB₃, YG₃, YG₄, YG₅}

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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 B1, B2 and G1, G2 respectively. Let us denote 1 boy and 3 girls in room Y as B3, and G3, G4, G5 respectively. Accordingly, the required sample space is given by S = {XB1, XB2, XG1, XG2, YB3, YG3, YG4, YG5}

Let us denote 2 boys and 2 girls in room X as B₁, B₂ and G₁, G₂ respectively. Let us denote 1 boy and 3 girls in room Y as B₃, and G₃, G₄, G₅respectively.

Accordingly, the required sample space is given by S = {XB₁, XB₂, XG₁, XG₂, YB₃, YG₃, YG₄, YG₅}