Four electronic ovens that were dropped during shipment are inspected and classi

Question

Four electronic ovens that were dropped during shipment are inspected and classified as containing either a major, a minor, or no defect. In the past, 50% of the dropped ovens had a major defect, 20% had a minor defect and 30% had no defect. Assume that the defects on the four ovens occur independently. Determine the following. Round your answers to four decimal places (e.g. 98.7654). The conditional probability that two ovens have major defects given that two ovens have minor defects. The conditional probability that three ovens have major defects given that two ovens have minor defects. The conditional mean of the number of ovens with major defects given that two ovens have minor defects.

Explanation / Answer

a. P(2 major | 2 minor) = P(2 major and 2 minor) / P(2 minor)

= 4C2*0.52 *2C2*0.22 / [4C2*0.22]

= 0.25

b. P(3 major | 2 minor) = P(3 major and 2 minor) / P(2 minor)

= 0 [As out of 4 ovens, 3 major and 2 minor are not possible]

c. P(0 major | 2minor) = P(0 major and 2 minor) / P(2 minor)

= 4C2*(1-0.5)2 *2C2*0.22 / 4C2*0.22

= 0.25

P(1 major | 2minor) = P(1 major and 2 minor) / P(2 minor)

= 4C1*0.5*3C1*(1-0.5) *2C2*0.22 / 4C2*0.22

= 0.50

P(2 major | 2 minor) = P(2 major and 2 minor) / P(2 minor)

= 4C2*0.52 *2C2*0.22 / [4C2*0.22]

= 0.25

So, Mean:

E[Major | 2 minors] = 0*0.25 + 1*0.50 + 2*0.25

= 1

Answers:

a. 0.25

b. 0

c. 1

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