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?

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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.

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