Question: Find the probabilities for the following discrete random variables (20 pts)

a. A large company has an inspection system for the batches of small compressors purchased from vendors. A batch typically contains 15 compressors. In the inspection process, a random sample of 5 is selected and all are tested. Suppose there are 2 faulty compressors in the batch of 15. What is the probability that for a given sample, there will be 1 or less faulty compressors?

b. An oil drilling company ventures into various locations, and their success or failure is independent from one location to another. Suppose that the probability of a success at any specific location is .25. Also suppose that the drilling company feels that it will “hit it big” if the second success occurs before the sixth attempt. What is the probability that the driller will “hit it big.”

c. The potential buyer of a particular engine requires that the engine start successfully 10 consecutive times. Suppose that the probability of a successful start is .990. Consider that the outcomes of attempted starts is independent. What is the probability that the engine is accepted after just 10 starts?

d. An electronic switching device occasionally malfunctions and may need to be replaced. It is known that the device is satisfactory if it makes, on average no more than .2 errors per hour. A particular five hour period is chosen as a “test” on the device. If no more than 1 error occurs, the device is considered satisfactory. What is the probability that a satisfactory device will be mis- diagnosed as “unsatisfactory” on the basis of the test?

e. A restaurant chef prepares a tossed salad containing, on average, 5 vegetables per day. Find the probability that the salad contains more than 5 vegetables on i) a given day and on ii)3 of the next 4 days?