In class 10A, there are 20 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?

Total number of students = 80

i. Probability of both being girl.

For both being a girl i.e. girl is selected from class 10A and another girl is selected from class 10B

Total number of girls = 45

Probability of both being girls

ii. Probability of both being boys

For both being a boy i.e. boy is selected from class 10A and another boy is selected from class 10B

Total number of boys = 35

Probability of both being boys

iii. Probability of one boy and one girl

For one boy and one girl, a boy is selected from class 10A and a girl from class 10B or vice a versa.

i.e. P (boy from class 10A) × P (girl from class 10B) +

P (girl from class 10A) × P (boy from class 10B)

⇒

⇒

⇒

= 0.50

Probability of one boy and one girl is 0.50.

iv. Probability of at least one boy.

For at least one boy means one boy and another girl, or both boy.

In this, one boy and other girl can occur in two ways:

1^st boy and 2^nd girl or the other way round.

(20 × 25) + (20 × 15)

= 500 + 300

= 800

∴ the possibility is 0.50 (obtained in previous part)

We have already seen the possibility of both the boys in above solved parts i.e. probability of both boys is 0.4375

∴ Probability of at least one boy = 0.50 + 0.4375

= 0.9375