1) A factory is production cars, assembly line A produces 5% hybrid cars, assemb
ID: 3073825 • Letter: 1
Question
1) A factory is production cars, assembly line A produces 5% hybrid cars, assembly line B produces 8% hybrid cars, and assembly line C produces 10% hybrid cars. Of the total output from these machines, 45% of the items are from machine A, 30% from B, and 25% from C. One car is selected at random from a day's production for inspection. Calculate P[D], the probability that the car is hybrid. If inspection finds the item to be hybrid, what is the revised probability that the item came from Assembly line C? If inspection finds the item to be hybrid, what is the revised probability that the item came from Assembly line B? If inspection finds the item to be hybrid, what is the revised probability that the item came from Assembly line A?Explanation / Answer
A: Random car came from Assembly line A, P(A) = 0.45
B: Random car came from Assembly line B, P(B) = 0.30
C: Random car came from Assembly line C, P(C) = 0.25
D: Random car is a hybrid
P(D|A) = 0.05
P(D|B) = 0.08
P(D|C) = 0.10
A random car is selected for inspection.
Probability that the car is hybrid, P(D) , Using total law of probability:
P(D) = P(A)P(D|A) + P(B)P(D|B) + P(C)P(D|C)
P(D) = (0.45 x 0.05) + (0.30 x 0.08) + (0.25 x 0.10) = 0.0715
Next,
Probability that the item came from Assembly line C given that the inspection finds the item to be hybrid, i.e. P(C|D)
P(C|D) = P(CD) / P(D) = P(C)P(D|C) / P(D)
P(C|D) = (0.25 x 0.10) / 0.0715 = 0.349
Probability that the item came from Assembly line B given that the inspection finds the item to be hybrid, i.e. P(B|D)
P(B|D) = P(BD) / P(D) = P(B)P(D|B) / P(D)
P(B|D) = (0.30 x 0.08) / 0.0715 = 0.336
Probability that the item came from Assembly line A given that the inspection finds the item to be hybrid, i.e. P(A|D)
P(A|D) = P(AD) / P(D) = P(A)P(D|A) / P(D)
P(A|D) = (0.45 x 0.05) / 0.0715 = 0.315
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