Question

"The probability that a certain type of battery in a smoke alarm will last 4 years or more is .65. The probability that a battery will last 7 years or more is .10. Suppose that the battery is 4 years old and is still working, what is the probability that the battery will last at least 7 years?"

Answer 1

Answer:

15.38% probability that the battery will last at least 7 years

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

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

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Lasting 4 years or more.

Event B: Lasting 7 years or more.

The probability that a certain type of battery in a smoke alarm will last 4 years or more is .65.

This means that $P(A) = 0.65$

Intersection:

The intersection between 4 years or more and 7 years or more is 7 years or more.

The probability that a battery will last 7 years or more is .10, which means that $P(A \cap B) = 0.1$

What is the probability that the battery will last at least 7 years?

$P(B|A) = \frac{0.1}{0.65} = 0.1538$

15.38% probability that the battery will last at least 7 years