-A fair die is tossed twice (a die is said to be fair if all outcomes 1,...,6 ar
ID: 3061246 • Letter: #
Question
-A fair die is tossed twice (a die is said to be fair if all outcomes 1,...,6 are equally likely). Given that a 3 appears on the first toss, what is the probability of obtaining the sum 7 after the second toss?
-Assume there are three machines A, B, and C in a semiconductor manufacturing facility that make chips. They manufacture, respectively, 25, 35, and 40 percent of the total semiconductor chips there. Of their outputs, respectively, 6, 4, and 2 percent of the chips are defective. A chip is drawn randomly from the combined output of the three machines and is found defective. What is the probability that this defective chip was manufactured by machine A? by machine B? by machine C?
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Explanation / Answer
A die has 6 sides. Hence, a fair die would have 1/6 probability of each number. Since 3 already appeared on the first toss, we would need to have 4 on the second toss to have the total to 7. The probability of having a 4 is 1/6. Hence, the correct answer is 1/6.
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