Company XYZ produces widgets on two machines Machine 1 and M

Company XYZ produces widgets on two machines, Machine #1 and Machine #2. The production breakdown and yield rates are given below:
-Machine #1 produces 85% of the widgets, 96% meet specifications.
-Machine #2 produces 15% of the widgets, 85% meet specifications.

A) A widget is randomly selected from company XYZ, what is the probability that the widget will meet specifications?

B) Given that a widget selected at random meets specifications, what is the probability that it came from Machine 1?

Solution

A)

Probability of a widget to meet specification = P (Machine) * P(Spec)

= 0.85 * 96 + 0.15 * 85

= 94.35% widgets meet specification.

B)

It\'s given that the widget meets specification, thus the sample size is reduced to 94.35%

Now to find the probability of whether it is from machine 1

= (0.85 * 96) / 94.35

= 32/37

= 86.48 %

Hope this helps. Thanks