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"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?"

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Answer:

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

Explanation:

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


P(B|A) = (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) = (0.1)/(0.65) = 0.1538

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

User Louis Van Tonder
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