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, orno defect. In the past, 60% of the dropped ovens had a majordefect, 30% had a minor defect and 10% had no defect. Assume thatthe defects on the four ovens occur independently.

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

(b) What is the probability that no oven has a defect?

(c) What is the expected number of ovens with a major defect?

(d) What is the expected number of ovens with a major defect?

and....

Four electronic ovens that were dropped during shipment areinspected and classified as containing either a major, a minor, orno defect. In the past, 60% of the dropped ovens had a majordefect, 30% had a minor defect and 10% had no defect. Assume thatthe defects on the four ovens occur independently. Determine thefollowing:

(a) The conditional probability that two ovens have major defectsgiven that two ovens have minor defects.

(b) The conditional probability that three ovens have major defectsgiven that two ovens have minor defects.

(c) The conditional mean of the number of ovens with major defectsgiven 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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