Question

A machine is made of two parts, gizmos and widgets. the probability that a gizmo is defective is 0.20, and the probability that a widget is defective is .25. if a machine is assembled with one gizmo and one widget, what is the probability that the machine will not have any defective parts?

Answer 1

Given that the probability that:
Gizmo is defective is 0.20
widget is defective is 0.25

The probability that:
Gizmo is not defective is 1-0.2=0.8
Widget is not defective is 1-0.25=0.75

If the machine is assembled with only one gizmo and one widget, the probability that the will not have any defective part is:
P(Widget is not defective)*P(Gizmo is not defective)
=0.8*0.75
=0.6