The firm that manufactures patriot missiles purchases the guidance circuits from three different suppliers. Supplier A...

The firm that manufactures patriot missiles purchases the guidance circuits from three different suppliers. Supplier A provides 30% of the guidance circuits and those circuits have a fault probability of pA =0.02, whereas the circuits from supplier B, which provides 25% of those purchased, have a fault probability of pB =0.025. The guidance circuits purchased from supplier C have pC =0.01. If a batch of 200 missiles is fired during a particular strategic offensive and three of the missiles fail to track to target, what is the probability that the batch of missiles contained guidance circuits obtained from supplier B?

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Expert Solution

P[ manufactures patriot missiles purchases the guidance circuits from supplier A ] = P[ A ] = 30% = 0.3

P[ manufactures patriot missiles purchases the guidance circuits from supplier B ] = P[ B ] = 25% = 0.25

P[ manufactures patriot missiles purchases the guidance circuits from supplier C ] = P[ C ] = 1 - P[ A ] - P[ B ] = 1 - 0.3 - 0.25 = 1 - 0.55 = 0.45

Let, F be the event that circuits have a fault

P[ circuits have a fault | manufactures patriot missiles purchases the guidance circuits from supplier A ] = P[ F | A ] = 0.02

P[ circuits have a fault | manufactures patriot missiles purchases the guidance circuits from supplier B ] = P[ F | B ] = 0.025

P[ circuits have a fault | manufactures patriot missiles purchases the guidance circuits from supplier C ] = P[ F | C ] = 0.01

P[ circuits have a fault ] = P[ F ] = P[ F | A ]*P[ A ] + P[ F | B ]*P[ B ] + P[ F | C ]*P[ C ]

P[ circuits have a fault ] = P[ F ] = 0.02*0.3 + 0.025*0.25 + 0.01*0.45

P[ circuits have a fault ] = P[ F ] = 0.006 + 0.0625 + 0.0045

P[ circuits have a fault ] = P[ F ] = 0.073

P[ missiles fail to track to target, what is the probability that the batch of missiles contained guidance circuits obtained from supplier B ] = P[ B | F ]

P[ B | F ] = ( P[ F | B ]*P[ B ] )/P[ F ]

P[ B | F ] = 0.025*0.25 / 0.073

P[ B | F ] = 0.0625/0.073

P[ B | F ] = 0.8562

P[ missiles fail to track to target, what is the probability that the batch of missiles contained guidance circuits obtained from supplier B ] = 0.8562

milcah answered 7 months ago

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