Given: 2 boys and 2 girls are in room P and 1 boy 3 girls are in room Q.

To Find: Write the sample space for the given experiment.

Explanation: Let us denote two boys and girls in room P as B₁ , B₂ and G_{1 ,} G₂ respectively

Let us denote 1 boy and 3 girls in room Q as B₃ and G₃, G₄, G₅ respectively.

According to the question,

Sample spaces for room S_p are

S_p={(P, B₁), (P, B₂), (P, G₁), (P, G₂)}

And, Sample spaces for room S_q are

S_q={(Q, B₃), (Q, G₁), (Q, G₂), (Q, G₃)}

Now, The total sample spaces for the given experiment:

S=

S={(P, B₁), (P, B₂), (P, G₁), (P, G₂), (Q, B₃), (Q, G₁), (Q, G₂), (Q, G₃)}

Hence, S is the sample space for the given experiment