Answer to Question #91891 in Statistics and Probability for Nancy

Question

Machines A, B, and C all produce the same two parts, X and Y. Of all the parts
produced, machine A produces 60%, machine B produces 30%, and machine C
produces 10%.
In addition,
40% of the parts made by machine A are part X.
50% of the parts made by machine B are part X.
70% of the parts made by machine C are part X.
A part produced by this company is randomly sampled and is determined to be an X
part. With the knowledge that it is an X part, revise the probabilities that the part
came from machine A, B, or C.


Answere this with solution

Answer 1

P(A) = 0.6

P(B) = 0.3

P(C) = 0.1

P(X | A) = 0.4

P( X | B) = 0.5

P(X | C ) = 0.7

P(X) = P(X | A) P(A) + P(X | B) P(B) + P(X | C) P(C) = 0.46

P(X | A) P(A) = P(A | X) * P(X) ->

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

P(B | X) = P(X | B) P(B) / P(X)

P(C | X) = P(X | C) P(C) / P(X)

P(A | X) = 0.521

P(B | X) = 0.326

P(C | X) = 0.152

Answer: P(A | X) = 0.521, P(B | X) = 0.326, P(C | X) = 0.152.