5.80 Problems with Your New Smartphone? A new study by Square Trade indicates that smartphones are 50% more likely to malfunction than simple phones over a three-year period.14 Of smartphone failures, 30% are related to internal components not working, and overall, there is a 31% chance of having your smartphone fail over three years. Suppose that smartphones are shipped in cartons of N=50 phones. Before shipment, n = 10 phones are selected from each carton, and the carton is shipped if none of the selected phones are defective. If one or more are found to be defective, the whole carton is tested.

a. What is the probability distribution of X, the number of defective phones related to internal components not working in the sample of n = 10 phones?

b. What is the probability that the carton will be shipped if two of the N = 50 smartphones in the carton have defective internal components?

c. What is the probability that the carton will be shipped if it contains four defectives? Six defectives?