Assume that company A makes 80% of all electrocardiograph machines in the market
ID: 3355508 • Letter: A
Question
Assume that company A makes 80% of all electrocardiograph machines in the market, company B makes 15% of them, and 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 tested and is found to be defective. Find the probability that it was made by company A (b) Suppose we randomly select one electrocardiograph machine from the market. Find the probability that it was made by company A and it is not defective.Explanation / Answer
a)
probability of machine to be defective =P(from company A and defective+from company B and defective+from company C and defective)=0.80*0.04+0.15*0.05+0.05*0.08=0.0435
hence probability of machine manufactured made by company given defective
=P(from company A and defective)/P(dfective) =0.80*0.04/0.0435=0.7356
b) probability made by company and not defective =P(company A)*P(not defective|company A)
=0.8*(1-0.04)=0.768