Question

Suppose there is a 20% chance that revenue will exceed expectations, a 10% chance that costs will be lower than expected, and a 25% chance that the number of defective parts will be lower than expected. Assume that all variables are statistically independent. What is the chance that all 3 favorable outcomes occur together?

Answer 1

The chance that all 3 favorable outcomes occur together is 0.005

Explanation:

When two events are independent, the probability of both occurring is the product of the probabilities of the individual events. More formally, if events A and B are independent, then the probability of both A and B occurring is:

P(A and B) = P(A) x P(B)

In this case,

P(A) =P(revenue will exceed expectations)=20%

P(B) = P(costs will be lower than expected)= 10%

P(C)= P(number of defective parts will be lower than expected)=25%

P(A and B and C) = P(A) x P(B) x P(C)

P(A and B and C) = 0.20x0.10x0.25=0.005