MATH SOLVE

3 months ago

Q:
# A computer company manufactures chips in three facilities. Chips from facilities A, B, and C are defective with probabilities 0.004, 0.005, and 0.003 respectively. Assume that the proportions of chips from A, B, and C are 0.3, 0.3, and 0.4 respectively. (a) What is the probability that a randomly selected chip is defective? (b) If a randomly selected chip is found to be defective, what is the probability that it came from facility B? (c) If a randomly selected chip is found to be defective, what is the probability that it came from facility C?

Accepted Solution

A:

Answer:a) 0.012b) 0.036c) 0.048Step-by-step explanation:a)
If we take a random sample of 1,000 chips, there must be
1,000*0.004= 4 defective chips from facility A
1,000*0.005= 5 defective chips from facility B
1,000*0.003= 3 defective chips from facility C.
So, in a random sample of 1,000 chips there must be 12 defective chips, hence the probability that a randomly selected chip is defective is
12/1000 = 0.012 b)
The probability that a chip is defective and came from B is P(the chip is defective)*P(the chip came from B)=
0.012*0.3 = 0.036
c)
The probability that a chip is defective and came from C is P(the chip is defective)*P(the chip came from C)=
0.012*0.4 = 0.048