Question

Sonali can solve 70% of the problems in a competitive exam and Nirali can solve only 60% in the same exam. What is the probability that at least one of them will solve a problem, provided selection of questions is done randomly from the same exam ?

• A. 0.82
• B. 0.88
• C. 0.62
• D. 0.72

Answer 1

The Correct Option is B

In the given problem, Sonali can solve 70% of the problems, and Nirali can solve 60% of the problems in a competitive exam. We need to find the probability that at least one of them will solve a problem.

First, let's denote:

• P(S) as the probability that Sonali solves a problem = 0.7
• P(N) as the probability that Nirali solves a problem = 0.6

The probability that Sonali does not solve the problem is:

P(S') = 1 - P(S) = 1 - 0.7 = 0.3

The probability that Nirali does not solve the problem is:

P(N') = 1 - P(N) = 1 - 0.6 = 0.4

The probability that neither Sonali nor Nirali solves the problem is:

P(S' ∩ N') = P(S') × P(N') = 0.3 × 0.4 = 0.12

The probability that at least one of them solves the problem is the complement of both not solving it:

P(S ∪ N) = 1 - P(S' ∩ N') = 1 - 0.12 = 0.88

The probability that at least one of them will solve the problem is 0.88.