2. In a shipment of 15 room air conditioners, there are 3 with defective thermostats. Two air conditioners will be selected at random and checked one after another. Find the probability that

1. the first is defective
2. the first is defective and the second is good.
3. both are defective
4. the second one is defective
5. exactly one of the 2 is defective
6. at least one is defective.

3. Assume that 3 air conditioners (as in problem 2) are inspected. Find the probability that

1. all 3 are good.
2. the first 2 are good and the is defective.
3. two are good and one is defective.

4. A paint store sells three types of high volume paint sprayers used by professional painters: type I, type II, and type III. Based on records, \(70 \%\) of the sprayers are of type I, and \(20 \%\) are of type II. \(3 \%\) of the type I sprayers need repair during the warranty period, while the figure for type II is \(4 \%\), and the figure for type III is \(5 \%\). Label the events you will use in this problem and state their probabilities.

1. Find the probability that a randomly selected sprayer will need repair under warranty.
2. Find the probability that two randomly selected sprayers will need repair under warranty. Hint: think about independence.
3. Find the probability that a sprayer is of type III, given that it needed repair during the warranty period.

6. A survey report states that \(70 \%\) of adult women visit their doctors for a physical exam at least once in the last two years. If 20 adult women are randomly selected, find the probability that

1. fewer than 14 of them had a physical exam in the past two years.
2. at least 17 of them had a physical exam in the past two years.

7. Suppose that of college seniors support an increase in federal funding for the elderly. If 60 college seniors are randomly selected, what is the probability that at most 15 of them support the increased funding? (Go for an exact value.)

8. Use a normal approximation in the following problem. Use the continuity correction and interpolation (if needed).

A survey revealed that of the adult American population were regular users of alcoholic beverages. A random sample of 1000 adults is taken. Find the probability that

1. exactly 300 are regular users.
2. less than 280 are regular users.
3. 316 or more are regular users.

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