A manufacturing firm employs three analytical plans for desi

A manufacturing firm employs three analytical plans for design and development of a particular product For cost reasons, all three plans are used at varying times. In fact, plans A, B and C are used for 30%, 20% and 50% of the products, respectively. It is also known from past experience that 2% of the products using plan A will be defective. Similarly, the product defective rate for plan B and C are 3% and 1% respectively. Suppose that a finished product is randomly selected. What is the probability that it will be defective? If a randomly selected product is found to be defective, which plan was most likely used? Clearly explain your answer.

Solution

By using the Bayes Probability Law

(a) 0.017

(b) Plan C was most likely used.

Event	Prior Prob.	Conditional Prob.	Joint Prob.	Posterior Prob.
A	0.3	0.02	0.006	0.3529
B	0.2	0.03	0.006	0.3529
C	0.5	0.01	0.005	0.2942
		Total	0.017