Question 1159315: A manufacture of air-conditioning units purchases 70% of its thermostats from company A, 20% from company B, and the rest from company C. Past experience shows that 5% of company A’s thermostats, 1% of company B’s thermostats and 1,5% of company C’s thermostats are likely to be found to have a defective thermostat.
6.1 find the probability that company A supplied the defective thermostat. (8)
6.2 find the probability that company B supplied the defective thermostat. (8)
Answer by ikleyn(52886)   (Show Source):
You can put this solution on YOUR website! .
As it is worded and presented in the post, the problem is posed incorrectly.
The corrected formulation (corrected by me) is as follows:
A manufacture of air-conditioning units purchases 70% of its thermostats from company A, 20% from company B,
and the rest from company C. Past experience shows that 5% of company A’s thermostats, 1% of company B’s thermostats
and 1,5% of company C’s thermostats are likely to be found to have a defective thermostat.
One thermostat was chosen randomly, and it was defective. <<<---===
6.1 find the probability that company A supplied the defective thermostat. (8)
6.2 find the probability that company B supplied the defective thermostat. (8)
Solution
Let N be the total number of thermostats purchased from companies A, B and C.
0.7N thermostats are from company A,
0.2N thermostats are from company B, and
0.1N thermostats are from company C.
Of 0.7N thermostats from company A, 5% are defective, i.e. 0.05(0.7N) = 0.035N.
The number of all defective thermostats is 0.05*(0.7N) + 0.01*(0.2N) + 0.015*(0.1N)
Therefore, the probability that randomly selected defective thermostat came from company A is
 =  = 0.636364. ANSWER
Solved.
With the second question, do the same.
------------------
Hey, why I should make corrections in your posts ?
It is your job and your responsibility to present them in ideal conditions (!)
|
|
|
