2) An ice chest contains 6 cans of apple juice, 9 cans of grape juice, 8 cans of

Question

2) An ice chest contains 6 cans of apple juice, 9 cans of grape juice, 8 cans of orange juice, and 4 cans of pineapple juice. Suppose that you reach into the container and randomly select three cans in succession. a) What is the probability that all of the three are grape juice? b) What is the probability that none of the three are orange juice? c) What is the probability that at least one of the three is pineapple juice? You are taking a multiple-choice test that has 10 questions. Each of the questions has 3 choices, with one correct choice per question. a) If you RANDOMLY select one of these answer options per question and leave nothing blank, what is the probability of answering 4 or fewer questions correctly? b) What is the probability of answering exactly S5 questions corectly? c) What is the probability of answering 6 or more questions correctly?

Explanation / Answer

(2)

Total number of juices = 6+9+8+4 = 27

Probability that all the three are grape juice = 9C3/27C3 = 0.0287

Probability that none of the three are orange juice = 19C3/27C3 = 0.331

Probability that atleast one of the three is pineapple = 1 - Probability that none of the three is pineapple juice

Probability that none of the three is pineapple juice = 23C3/27C3 = 0.605

So,

Probability that atleast one of the three is pineapple = 1-0.605 = 0.395

Hope this helps !

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