There are three boxes. Box 1 contains one white ball and two black balls; box 2

Question

There are three boxes. Box 1 contains one white ball and two black balls; box 2 contains two white balls and one black ball; box 3 contains two white balls and three black ones. Someone selects one ball randomly from each box. So totally, three balls are taken out from three boxes. Find the probability that there are exactly one white ball among selected 3 balls. Your come to visit you. Suppose that he will come by train with probability 1/6; by ship, car, or plane with probabilities 1/6, 1/6, or 1/2, respectively. If the probability is 1/4 that he will be late by train; 1/3, 1/12 by ship, car, respectively; 0 by plane. Suppose we knew that he was late for the visit. What is the probability that he came by train? Suppose we knew that he was not late for the visit. What is the probability that he came by train? 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 0.6 and 0.5, 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. What is the probability that a randomly chosen flashlight will give more than 100 hours of use? Given that a flashlight lasted over 100 hours, what is the conditional probability that it was a type 1 flashlight?

Explanation / Answer

Question 1)

Total no.of balls = 11

Total no.of white balls = 5

P(Exactly one white ball) = 5C1 / 11C3

   = 5 / 165

= 0.0303

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