27.03.2023 - 19:31

A bin contains 3 different types of disposable flashlights. The probability that a type 1 flashlight will give over 100 hours of use is 0.8, with the corresponding probabilities for type 2 and type 3 flashlights being 0.5 and 0.4, respectively. Suppose th

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A bin contains 3 different types of disposable flashlights. The probability that a type 1 flashlight will give over 100 hours of use is 0.8, with the corresponding probabilities for type 2 and type 3 flashlights being 0.5 and 0.4, respectively. Suppose that 50 percent of the flashlight in the bin are type 1, 30 percent are type 2, and 20 percent are type 3.

A. What is the probability that a randomly chosen flashlight will give more than 100 hours of use?

B. Given that a flashlight lasted over 100 hours, what is the conditional probability that it was a type 1 flashlight?

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