Math1313-Section7.6-Blank - All the refrigerators are...

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Section 7.6 Bayes’ Theorem In Section 7.5 we discussed the conditional probability of the occurrence of an event, given the occurrence of an earlier event. Now we are going to reverse the problem and try to find the probability of an earlier event conditioned on the occurrence of a later event. We can use a principle called Bayes’ Theorem to solve problems of this type. This theorem is an application of conditional probability. We’ll use the conditional probability formula and the product rule to solve these problems. Example 1: A company produces 1,000 refrigerators a week at three plants. Plant A produces 350 refrigerators a week, plant B produces 250 refrigerators a week, and plant C produces 400 refrigerators a week. Production records indicate that 5% of the refrigerators produced at plant A will be defective, 3% of those produced at plant B will be defective, and 7% of those produced at plant C will be defective.
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Unformatted text preview: All the refrigerators are shipped to a central warehouse. If a refrigerator at the warehouse is found to be defective, what is the probability that it was produced at plant C? Section 7.6 – Bayes’ Theorem 1 Example 2: Suppose that from a well-shuffled deck of 52 playing cards two cards are drawn in succession, without replacement. What is the probability that the first card was a king, given that the second card was not a king? Example 3: A placement test is given by a certain high school to predict student success in a particular math course. On average, 70% of students who take the test pass it, and 87% of those who pass the test also pass the course, whereas 8% of those who fail the test pass the course. If a student passed the course, what is the probability that he or she did not pass the test? Section 7.6 – Bayes’ Theorem 2...
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