5. Assume that company A makes 80% of all electrocardiograph machines company B

Question

5. Assume that company A makes 80% of all electrocardiograph machines company B make 15% of them, and the company C makes the other 5%. The electrocardiographs machines made by company A have a 4% rate of defects, the company B machines have a 5% rate of defects, while the company C machines have a 8% rate of defects. (a) If a randomly selected electrocardiograph machine is then tested and is found to be defective. Find the probability that it was made by the company A (b) If a particular electrocardiograph machine is randomly selected from the general population of all such machines, find the proba bility that it was made by company A and it is not defective.

Explanation / Answer

a)

probability of defective =P(from company A and defective+from company B and defective+from company C and defective) =0.8*0.04+0.15*0.05+0.05*0.08 =0.0435

therefore probability made by company A given defective=P(from company A and defective)/P(defective)

=0.8*0.04/0.0435 =0.7356

b)

P(made by company A and not defective)= 0.8*(1-0.04)=0.768

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