Answer to Question #311287 in Microeconomics for Yonas

Question

Suppose an importer of medical devises imports ultrasound machines: 50% from X, 30% from Y, and 20% from Z. If 10% of the machines from X, 5% from Y, and 10% from Z are defective, (a) what is the probability that an ultrasound machine imported by the importer is defective? (b) if an ultrasound machine is found defective, what is the probability that it came from Z? 

Answer 1

solution

Let N represent the total number of devices bought.

The ratio bought from each company is as follows

$X=0.5 N$

$Y=0.3 N$

$Z =0.2Z$

(a) Let D represent the defective devices

$P(D)=0.1(0.5)+0.05(0.3)+0.1(0.2)$

$P(D)= 0.085$

(b) Let DZ represent defective devices from Z

$P(DZ)=\dfrac{0.1(0.2)}{0.1(0.5)+0.05(0.3)+0.1(0.2)}$

$P(DZ)=0.2353$