Telecom produces sets in 2 plants... (please check ans)

M

messanger123434

New member
Joined
Nov 5, 2008
Messages
9
A telecom produces telephone sets in two plants: New York, and Buffalo. Daily production volumes of a certain model are : 500 and 2000 units respectively. From past experience it is known that the defective percentages are: 0.5% and 1% respectively.

If all the output of this telephone mode, from the two plants is stored in a regional warehouse.
A telephone is drawn at random and found to be defective.
What is the probability that it would be from plant in New York?
What is the probability that it would be from plant in Buffalo?
What is the probability that it would be from plant in Albany?

Solution:

No. of telephones of a certain model produced in the New York Plant = 500 units

No. of telephones of a certain model produced in the Buffalo Plant = 2000 units

Total No. of telephones of a certain model produced in both the plants are: 500 + 2000 = 2500 units

No. of defective telephones of a certain model in New York Plant are: 0.5% of 500 = 2.5 units

No. of defective telephones of a certain model in Buffalo Plant are: 1% of 2000 = 20 units

Total No. of defective telephones of a certain model produced in both the plants are: 2.5 + 20 = 22.5 units

A telephone is drawn at random and found to be defective

a. Probability that it would be from a plant in New York is:
(No. of defective telephones in NY plant) / (Total no. of defective telephones produced in both plants) = 2.5 / 22.5 = 0.1111

b. Probability that it would be from a plant in Buffalo is:
(No. of defective telephones in Buffalo plant) / (Total no. of defective telephones produced in both plants) = 20 / 22.5 = 0.8889

c. Probability that it would be from a plant in Albany is: 0 (as no telephones were produced in the Albany plant)
 
It looks right, given that you are limiting the possible outcomes to defective phones. If you know the phone is defective, then you can ignore all the working phones in your denominator, and since one plant has a higher defect rate and provides more phones overall, its probability is higher. If you don't know the phone is defective, however, the probabilities are simply 0.8 and 0.2.

Another slant on this problem would be to calculate the probability of getting a phone from Buffalo and then finding that phone to be defective. This is a different problem, and it's how I first read the problem, because if you were an auditor, you wouldn't know in advance which phones were defective. You would pick one out at random from the warehouse and then test it to find out if it was defective:

Probability of getting a phone from Buffalo in a random draw: 2000 / 2500 = 0.8
Probability that a phone from Buffalo is defective: 0.01 (given)

Answer to my question: 0.8 x 0.01 = 0.008

But if you know you've got a defective phone in your hands, there's an 89% probability that it came from Buffalo at this regional warehouse.

Finally, be careful about giving answer that say 22.5 phones are defective. I don't know what it means if you tell me half a phone is defective, so we might as well not make this a story problem if we can't get the context right.
 
You must log in or register to reply here.
Top