Question

A business assigned two different employees to work on a question independently. The company thinks the chance the first employee solves the problem is 0.9 and the probability the second employee solves the problem is 0.8. Assuming the success [or failure] of the employees is independent, what is the probability at least one of the employees will solve the problem?

Answer 1

0.98

Explanation:

The probability one or the other will solve the problem is ...

p(A or B) = p(A) + p(B) - p(A&B)

For independent events, ...

p(A&B) = p(A)p(B)

so, the probability of interest is ...

p(A or B) = 0.9 + 0.8 - 0.9·0.8 = 0.98

The probability is 0.98 that at least one of the employees will solve the problem.