Question

In class 10A, there are 30 boys and 20 girls. In 10B, there are 15 boys and 25 girls. One student is to be selected from each class.

i. What is the probability of both being girls?
ii. What is the probability of both being boys?
iii. What is the probability of one boy and one girl?
iv. What is the probability of at least one boy?

Answer 1

i. Total no. of possible pairs $=50\times 40=2000$
No. of pairs in which both are girls $=20\times 25=500$
Probability of both being girls $=\frac{500}{2000}=\frac{1}{4}$
ii No. of pairs in which both are boys $=30\times 15=450$
Probability of both being boys $=\frac{450}{2000}=\frac{9}{40}$
iii. No. of pairs in which one is boy and one is girl $=2000-(500+450)$ $=2000-950=1050$
Probability of one being boy and one girl $=\frac{1050}{2000}=\frac{21}{40}$
iv. No. of pairs in which at least one is boy $=1050+450=1500$
Probability in which at least one is boy $=\frac{1050}{2000}=\frac{3}{4}$