Question

An aircraft emergency locator transmitter (ELT) is a device designed to transmit a signal in the case of a crash. The ACME Manufacturing Company makes 70% of the ELTs, the B. BUNNY Company makes 25% of them, and the W. E. COYOTE Company makes the other 5%. The ELTs made by ACME have a 3.5% rate of defects, the B. BUNNY ELTs have a 5% rate of defects, and the W. E. COYOTE ELTs have a 8% rate of defects (which helps to explain why W. E. COYOTE has the lowest market share).

a) If a locator is randomly selected from the general population of all locators, find the probability that it was made by the ACME Manufacturing Company.

b) If a randomly selected locator is then tested and is found to be defective, find the probability that it was made by the ACME Manufacturing Company.

Answer 1

An aircraft emergency locator transmitter is a device designed to transmit a signal in the case of a crash.

The ACME Manufacturing company makes 70% of the ELTs, the B. Bunny company makes 25% of them, and W. E. Coyote company makes the other 5%.

The rate of defect in the ELTs of ACME company is 3.5%, the rate of defect in the ELTs of B.Bunny Company is 5%, and the rate of defect in the ELTs of W. E. Coyote company is 8%.

Now, let us define

A = Event that a randomly selected ELT is manufactured by ACME company

B = Event that a randomly selected ELT is manufactured by B. Bunny company

W = Event that a randomly selected ELT is manufactured by W. E. Coyote company

D = Event that a randomly selected ELT is defective.

The following are given.

Part (a)

If a ELT is randomly selected from the general poulation of all ELTs, find the probability that it was manufactured by ACME Manufacturing company.

So, we want to find P(A).

So, the answer to this question is

Part (b)

If a randomly selected locator is tested and found to be defective, what is the probability that it was manufactured by ACME Manufacturing company ?

First, we find out, what is the probability that a randomly selected ELT is defective.

We use the total probability theorem, to find this out.

Now, we have to find

By Bayes' theorem, we can write this as

which is approximately 0.60.

So, the answer is 0.5976, which when rounded off, is approximately 0.60.