Question

In a class there are 15 boys and 10 girls. Two students are selected at random. What is the probability of selecting one boy and one girl?
1. 1/3
2. 1/2
3. 1/4
4. 1/5

Answer 1

Correct Answer - Option 2 : 1/2

Given:

Numbers of boys = 15

Numbers of girls = 10

Total numbers of boys and girls = 15 + 10 = 25

Selected at random = 2

Formula Used: 

Probability = (Possible Outcome/Total Outcome)

ⁿC_r = n!/(n - r)! r!

Calculation:

Random selection of a boy 

⇒ ¹⁵C₁ = 15

Random selection of a girl 

⇒ ¹⁰C₁ = 10

Probability of selection a boy and a girl 

⇒ (15C1 × 10C1)/²⁵C₂

⇒ 150/300

⇒ 1/2

∴ Probability of selection a boy and a girl is 1/2.