Question

A can solve 90% of the problems given in a book and B can solve 70%. What is the probability that at least one of them will solve a problem, selected at random from the book?

1. 0.16
2. 0.69
3. 0.97
4. 0.20

Answer 1

Correct Answer - Option 3 : 0.97

Concept:

when two independent A and B events occur.

then the probability of occurring of at least one event is given by:

P = 1 - (P(\({\rm{\bar A}}\)) × P(\({\rm{\bar B}}\)))

Calculation:

Given:

A can solve 90% of problems and B can solve 70% of problems.

Therefore, A and B are independent of each other.

P(A) = 0.90 and P(B) = 0.70

Therefore, P(at least one of them will solve a problem)  = 1 - (P(\({\rm{\bar A}}\)) × P(\({\rm{\bar B}}\)))

∴ P = 1 - [(1 - 0.9) × (1 - 0.7)] ⇒ 1 - 0.03

P = 0.97