"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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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:15.38% probability that the battery will last at least 7 yearsStep-by-step explanation:We use the conditional probability formula to solve this question. It is[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]In whichP(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] 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 [tex]P(A) = 0.65[/tex]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 [tex]P(A \cap B) = 0.1[/tex]What is the probability that the battery will last at least 7 years?[tex]P(B|A) = \frac{0.1}{0.65} = 0.1538[/tex]15.38% probability that the battery will last at least 7 years

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