SOLUTION: Factories A, B and C produce computers. Factory A produces 2 times as many computers as factory C, and factory B produces 7 times as many computers as factory C. The probability th

Algebra ->  Probability-and-statistics -> SOLUTION: Factories A, B and C produce computers. Factory A produces 2 times as many computers as factory C, and factory B produces 7 times as many computers as factory C. The probability th      Log On


   

Question 926430: Factories A, B and C produce computers. Factory A produces 2 times as many computers as factory C, and factory B produces 7 times as many computers as factory C. The probability that a computer produced by factory A is defective is 0.033, the probability that a computer produced by factory B is defective is 0.034, and the probability that a computer produced by factory C is defective is 0.049.
A computer is selected at random and it is found to be defective. What is the probability it came from factory C?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
While factory C produces 1000 computers,
1000%2A0.049=49 probably defective,
factory A produces 2%2A1000=2000 computers,
2000%2A0.033=66 probably defective, and
factory B produces 7%2A1000=7000 computers,
7000%2A0.034=238 probably defective.
So during that period, the number of defective computers produced is expected to be
49%2B66%2B238=353 ,
and of those 353 defective computers, 49 came from factory C.
So the probability that the randomly selected defective computer comes from factory C must be
49%2F353=about0.1388 (rounded)
Maybe you would like to round it to 0.193=19.3%25 ,
since the probability data given for each factory had only 2 significant digits.