SSC CGL 2023 PYQ — Question 30

The correct answer is Option 4 i.e. (1125×3⁸)/(8¹⁰)

Given that

A person can hit a target 5 times out of 8 shots.

then the probability of hitting a target = 5/8

and the probability of not to hit a target = (8- 5)/8 = 3/8

If he fires 10 shots, then 

The probability that he will hit the target twice = ¹⁰C₂ × (5/8)² × (3/8)^{(10 - 2)}

= ¹⁰C₂ × (5/8)² × (3/8)⁸ 

= [10!/(2! × 8!)] × 25 × 3⁸/8¹⁰

= [(10 × 9)/2] × 25 × 3⁸/8¹⁰

= 45 × 25 × 3⁸ /8¹⁰ = (1125×3⁸)/(8¹⁰)