A computer maker receives parts from three suppliers, S1, S2, and S3. Fifty percent come from S1, twenty percent from S2, and thirty percent from S3. Among all the
parts supplied by S1, 5% are defective. For S2 and S3, the portions of defective
parts are 3% and 6% respectively.
i. What portion of all the parts is defective?
ii. A customer complains that a certain part in her recently purchased computer
is defective. What is the probability that it was supplied by S2?

The Bayes' theorem is being used to compute the posterior probabilities. This is a way to measure probability distribution. It's being used to estimate the posterior probabilities using the prior probabilities. Following are the solution to the given question:

a)

By the law of total probability, every probability area is divided into .

b)

Using the Bayes' rule:

Therefore, the final answer is " and "

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7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above

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