Question

When a student was selected from a class consisting of 20 girls and some boys the probability of the student being a girl is 2/5. If 2 students are selected from the same class, what is the probability of them being both girls or both boys?  
1. 21/49
2. 23/49
3. 25/49
4. 27/49
5. None of these

Answer 1

Correct Answer - Option 3 : 25/49

GIVEN:

Girls = 20

Probability of selecting a girl = 2/5

CONCEPT:

For 'or' addition function is applied.

FORMULA USED:
P = Favorable outcomes/Total outcomes

ⁿC_r = n!/r!(n - r)!

CALCULATION:

Let there be x boys in the class.

A.T.Q

20/(20 + x) = 2/5

⇒ 100 = 40 + 2x

⇒ x = 30

Total students = 50

Probability of 2 girls = ²⁰C₂/⁵⁰C₂ = 190/1225

Probability of 2 boys = 30C2/50C2 = 435/1225

Required probability = 190/1225 + 435/1225 = 25/49

∴ The probability is 25/49.