Question

The probability that a new car battery functions for more than 10,000 miles is .8, the probability that it functions for more than 20,000 miles is .4, and the probability that it functions for more than 30,000 miles is .1. If a new car battery is still working after 10,000 miles, what is the probability that (a) its total life will exceed 20,000 miles

Answer 1

Answer:

There is a 50% probability that its total life will exceed 20,000 miles.

Step-by-step explanation:

To solve this question, we use the following formula:

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

In which P(A|B) is the probability of A happening, given that B has happened, $P(A \cap B)$ is the probability of A and B happening, and P(B) is the probability of B happening.

In this problem, we want:

The probability of the total life of the car battery exceeding 20,000 miles, given that it exceeded 10,000 miles.

$P(A \cap B)$ is the probability of exceeding 20,000 and 10,000 miles. It is the same as the probability of exceeding 20,000 miles(If it exceeded 20,000 miles, necessarily it will have exceeded 10,000 miles). So $P(A \cap B) = 0.4$

P(B) is the probability of exceeding 10,000 miles. So $P(B) = 0.8)$

So

$P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.4}{0.8} = 0.5$

There is a 50% probability that its total life will exceed 20,000 miles.