Question

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

Write the sample space for the experiment in which a room is selected and then a person.

Answer 1

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 G₁ , 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∪ S_q

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