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Probability of Increase Actions

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1) A box contain 90 good times and 10 bad items. Thus the probability of randomly choosing a good item from this box is 0.9. A second box also contains 90 good items and 10 bad items. An item is randomly selected from the second box and is placed in the first box. Does this action increase the likelihood of picking a good item from the first box? (this has application in quality control)

2) There are three car rental agencies in town (agencies 1,2 and3). agency 1 has 40% of the rental car business in this town, agency 2 has 25% of the business, and agency 3 has the res. Suppose 4% of the cars of agency 1 are unsafe, whereas the % of unsafe cars for agency 2 and 3 are 8% and 5% respectively. What percentage of the rental cars in this town are safe to drive?

3) An insurance company issue life insurance policies in three separate categories: standard, preferred, and ultra-preferred. Of the company's policy holders, 50% are standard, 40% are preferred, and 10% are ultra preferred. Each standard policy holder has probability of 0.01 of dying in the next year, each preferred policyholder has a probability 0.005 of dying in the next year, and each ultra-preferred policyholder has a probability of 0.001 of dying in the next year. What is the probability of randomly chosen policyholder will die next year?

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The probability of increase actions are examined.

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This would not increase the likelihood of picking a good item:
Probability of picking a good ...

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