conditional probability A certain manufacturer produces cars at two factories A
ID: 2952185 • Letter: C
Question
conditional probability A certain manufacturer produces cars at two factories A and B.Ten percent of the cars produced at factory A are found to bedefective. while 5% of the cars producted at factory B aredefective. If factory A produces 100,000 cars per year and factory Bproduces 50,000 cars per year, compute the following a)The probability of purchasing a defective car from themanufacturer b) If a car purchased from the manufaturer is defective, whatis the probabiliy that it came conditional probability A certain manufacturer produces cars at two factories A and B.Ten percent of the cars produced at factory A are found to bedefective. while 5% of the cars producted at factory B aredefective. If factory A produces 100,000 cars per year and factory Bproduces 50,000 cars per year, compute the following a)The probability of purchasing a defective car from themanufacturer b) If a car purchased from the manufaturer is defective, whatis the probabiliy that it cameExplanation / Answer
B = the event that the car is from factory B, and D = the event that the car is defective.Then P(A) = 2/3 and P(B) = 1/3. The probability of a defective car from factory A is P(D|A) =0.10. Likewise, P(D|B) = 0.05.
The law of total probability tells us:
P(D) = P(A)*P(D|A) + P(B)*P(D|B) = (2/3)*(0.10) + (1/3)*(0.05) = 0.083333 or 8.33%.
b) I'm not sure what the last part of this question is asking,but assuming the question is "what is the probability that it camefrom factory A?", the solution would be:
P(A|D) = P(A and D)/P(D) = P(D|A)*P(A)/P(D) = (0.10)*(2/3)/(0.08333) = 0.8 or about 80%.
Thus, if the car is defective, the probability that it camefrom factory A is 80% and the probability that it came from factoryB is therefore 20%.
Cheers!
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