Question

The factory quality control department discovers that the conditional probability of making a manufacturing mistake in its precision ball bearing production is 4 % 4\% 4% on Tuesday, 4 % 4\% 4% on Wednesday, 4 % 4\% 4% on Thursday, 8 % 8\% 8% on Monday, and 12 % 12\% 12% on Friday. The Company manufactures an equal amount of ball bearings ( 20 % 20\% 20%) on each weekday. What is the probability that a defective ball bearing was manufactured on a Friday?

Answer 1

The probability that a defective ball bearing was manufactured on a Friday is 0.375.

Explanation:

The conditional probability of an events X given that another event A has already occurred is:

`P(X|A)=(P(A|X)P(X))/(P(A))`

The information provided is as follows:

P (D|M) = 0.08

P (D|Tu) = 0.04

P (D|W) = 0.04

P (D|Th) = 0.04

P (D|F) = 0.12

It is provided that the Company manufactures an equal amount of ball bearings, 20% on each weekday, i.e.

P (M) = P (Tu) = P (W) = P (Th) = P (F) = 0.20

Compute the probability of manufacturing a defective ball bearing on any given day as follows:

`P(D)=P(D|M)P(M)+P(D|Tu)P(Tu)+P(D|W)P(W)\\+P(D|Th)P(Th)+P(D|F)P(F)`

`=(0.08* 0.20)+(0.04* 0.20)+(0.04* 0.20)+(0.04* 0.20)+(0.12* 0.20)\\\\=0.064`

Compute the probability that a defective ball bearing was manufactured on a Friday as follows:

`P(F|D)=((D|F)P(F))/(P(D))`

`=(0.12* 0.20)/(0.064)\\\\=0.375`

Thus, the probability that a defective ball bearing was manufactured on a Friday is 0.375.