Question

Three students are selected at random from a class, comprising of 25 boys and 20 girls. What is the probability that there are two boys and one girl, among those selected students?

1. 21/167
2. 24/167
3. 37/117
4. 27/167
5. 17/117

Answer 1

Correct Answer - Option 2 : 24/167

Given:

Number of boys in the class = 25

Number of girls in the class = 20

Number of students selected at random = 3

Formula Used:

The probability of occurrence of an event E, within a sample space S, is given by:

P(E) = n(E) / n(S)

where P(E) = probability of occurrence of the event E,

n(E) = number of times the event E occurs, and

n(S) = number of points in the sample space S.

Calculation:

Total number of students in the class = 20 + 25 = 45

The total number of ways of selecting three students from the class is given by

⁴⁵C₃ = 14190

∴ n(S) = 14190

Probability of selecting two boys from 25 boys is given by

²⁵C₂ = 300

Similarly, probability of selecting one girl from 20 girls is given by

²⁰C₁ = 20

∴ n(E) = 300 × 20 = 6000

∴ We obtain the probability of selecting two boys and one girl from the class as

6000/14190 = 20/473

∴ The probability of selecting two boys and one girl from the class comprising of 25 boys and 20 girls, is 20/473