Acomputer manufacturer uses chips from three sources. chips from sources a, b, and c are defective with probabilities 0.001, 0.005, and 0.01, respectively. if a randomly selected chip is found to be defective, what is the probability that the manufacturer was a; that the manufacturer was c. my clarification: assume that the computer manufacturer uses equal numbers of chips from each source.

a) 1/16

b) 5/8

Step-by-step explanation:

Let's abuse a little of the notation and also call the events A, B and C as

A= the chip comes from source A

B= the chip comes from source B

C= the chip comes from source C

Since the computer manufacturer uses equal numbers of chips from each source

P(A)=P(B)=P(C)=1/3

Let D be the event

D = the chip is defective

If a randomly selected chip is found to be defective, what is the probability that the manufacturer was A

Here we want to find P(A | D) the conditional probability that the chip comes from source A given that is defective.

By the Bayes' Theorem

If a randomly selected chip is found to be defective, what is the probability that the manufacturer was C

Applying the same theorem