Four electronic ovens that were dropped during ship- ment are inspected and classified as containing either a major, a minor, or no defect. In the past, 60% of dropped ovens had a ma- jor defect, 30% had a minor defect, and 10% had no defect. Assume that the defects on the four ovens occur independently.

(a) Is the probability distribution of the count of ovens in each category multinomial? Why or why not?

(b) What is the probability that, of the four dropped ovens, two have a major defect and two have a minor defect?

(c) What is the probability that no oven has a defect? Determine the following:

(d) The joint probability mass function of the number of ovens with a major defect and the number with a minor defect

(e) The expected number of ovens with a major defect

(f) The expected number of ovens with a minor defect (g) The conditional probability that two ovens have major defects given that two ovens have minor defects (h) The conditional probability that three ovens have major. defects given that two ovens have minor defects (i) The conditional probability distribution of the number of ovens with major defects given that two ovens have minor defects (j) The conditional mean of the number of ovens with major defects given that two ovens have minor defects.