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 ?
- 0.82
- 0.88
- 0.62
- 0.72
The Correct Option is B
Solution and Explanation
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.
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