Probability Question 1

The probability that a new microwave oven will stop working in less than 2 years is 0.05. The probability that a new microwave oven is damaged during delivery and stops working in less than 2 years is 0.04. The probability that a new microwave oven is damaged during delivery is 0.10. Given that a new microwave oven is damaged during delivery, what is the probability that it stops working in less than 2 years?

0.05

0.10

0.40

0.50

Approach

We can use the formula for conditional probability.

P(A|B) = \frac{P(A\cap B)}{P(B)}

We are trying to find the probability that it stops working in less than 2 years, given that it is damaged during delivery.

P(\text{Stops Working}|\text{Damaged}) = \frac{P(\text{Stops Working}\cap \text{Damaged})}{P(\text{Damaged})}

P(\text{Stops Working}|\text{Damaged}) = \frac{0.04}{0.10} = \boxed{0.40}