Question

In a factory, only two machines, A and B, manufacture washers. Neither machine is perfect: machine A produces defective washers 10% of the time, while machine B produces defectives 4% of the time. Machine B is more efficient than machine A and accounts for 80% of the total output of washers. For purposes of quality control, a sample of washers is taken and examined for defectives. Compute the probability that a randomly chosen washer found to be defective was manufactured by machine B. Round your answer to two decimal places.

Answer 1

Answer:

0.6154 or 61.54%

Step-by-step explanation:

Machine B output level= 80%

Machine A output level= 20%

Machine B defective rate = 0.04

Machine A defective rate = 0.10

The proportion of total washers that are defective is:

$D=0.8*0.04+0.2*0.1\\D=0.052$

Therefore, the probability that a randomly selected washer was manufactured by machine B, given that it is defective, is determined by the proportion of defective washers produced by machine B divided by the proportion of total defective washers:

$p=\frac{0.8*0.04}{0.052}\\p=0.6154=61.54\%$

The probability is 0.6154 or 61.54%.