Question

Say you’re a reliability engineer for an electronics manufacturer that forms larger systems out of smaller subassemblies. In a particular test that you perform, there’s a 0.42 likelihood that a subassembly survives more than 500 usage cycles. If a subassembly does not survive more than 500 usage cycles, then there is a 0.73 likelihood that it was manufactured by company A. What is the probability that a subassembly is not manufactured by company A and does not survive more than 500 cycles?

Answer 1

We are given here that:

P( survives > 500 usage cycles) = 0.42,
therefore P(does not survive 500 usage cycles) = 1 - 0.42 = 0.58

Also, we are given here that: P( A | does not survive 500 usage cycles) = 0.73
Therefore, P( not A | does not survive 500 usage cycles) = 1 - 0.73 = 0.27

Now using Bayes theorem, we have:
P( not A and does not survive 500 usage hours )

= P( not A | does not survive 500 usage cycles) * P(does not survive 500 usage cycles)

= 0.27*0.58

= 0.1566

Therefore 0.1566 is the required probability here.