Four electronic ovens that were dropped during shipment areinspected and classif

Question

Four electronic ovens that were dropped during shipment areinspected and classified as containing either a major, a minor, or no defect. In the past, 60% of the dropped ovens had a majordefect, 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 cuont 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 folllowing:

(d) The joint probablitity mass funtion of the number of ovens with a major decect 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 defts given that two ovens have minor defects.

Explanation / Answer

Part (a) begins with the idea that they are allindependent: .60*.60*.30*.30 = .0324 However, that is not the correct answer. The requestedprobability is calculated using the following: 4!/(2!2!) = 6, where 4 is the number of objects and each '2' is the number oftimes each individual probability in the calculation above was used(.60 twice and .30 twice). Take 6*.0324 = .1944 for the answer. Thanks for the original response to get the ballrolling.

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