Question

The company has two machines that produce certain items. Machine 1 produces 40 % of the the items, and machine 2 produces 60% of the items. Machine 1 produces 3% of defective items and machine 2 produces 5% of defective items.

a. The probability that a randomly selected produced item is defective is _________

b. If a randomly selected item is found to be defective, probability that it is produced on machine 2 is___________

Answer 1

Let us define the following events:

A: an item is produced by Machine 1;

B: an item is produced by Machine 2; and

D: an item is defective.

Now, we are given that Machine 1 produces 40% of the items and Machine 2 produces 60% of the items. Thus, we get:

P(A) = P(an item is produced by Machine 1) = 40% = 0.4

P(B) = P(an item is produced by Machine 2) = 60% = 0.6

Moreover, we are given that Machine 1 produces 3% of defective items and Machine 2 produces 5% of defective items. Thus, we get:

P(D|A) = P(defective | machine 1) = 3% = 0.03

P(D|B) = P(defective | machine 2) = 5% = 0.05

a.

The probability that a randomly selected item is defective is given by:

b.

If a randomly selected item is found to be defective, the probability that it is produced on machine 2 is given by:

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