Find the probabilities for the following discrete random variables (27 pts) a. Among a shipment of 5,000 tires, 1,000 are slightly blemished. If one purchases 10 of these tires, what is the probability that 3 or less (P (x 3)) will go into overtime? c. The probability that a person, living in a certain city, owns a dog is estimated to be 0.3. Find the probability that the tenth person randomly interviewed in that city is the sixth one to own a dog. d. A local drugstore owner knows that, on average, 100 people per hour stop by his store. Find the probability that in a given 3 minute period, more than 5 (P(x > 5) people enter the store. e. 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 misdiagnosed as "unsatisfactory" on the basis of the test? f. A restaurant chef prepares a tossed salad containing, on average, 5 vegetables per day. Find the probability that the salad contains more than 7 vegetables on i) a given day and on ii)3 of the next 6 days? g. A second stage smog device has been installed on 50 different industry firms in Los Angeles. An inspector plans to visit 10 randomly selected industrial firms to check the device for violations. Assume that 15 industrial firms violate smog regulations. What is the probability that 5 or less of the inspected firms will result smog violation h. A family decides to have children until it has three children of the same gender. | Assume P(boy) = P(girl) = .5. What is the pmf of X, the number of children in the family