Question

In a reliability test there is a 42% probability that a computer chip survives more than 500 temperature cycles. If a computer chip does not survive more than 500 temperature cycles, then there is a 73% probability that it was manufactured by company A. Let A be the event that the chip was "made by company A", and B be the event that a chip "survives 500 temperature cycles". That is A made by company A = " ", and B survives 500 temperature cycles = " ". What is the Probability that a computer chip is not manufactured by company A and does not survive more than 500 temperature cycles?

Answer 1

The probability is
`P(B' n A ' ) =` 16%

Explanation:

From the question we are told that

A is the event that the chip was "made by company A"

B is the event that a chip "survives 500 temperature cycles"

The probability that a computer chip survives more than 500 temperature cycles is

`P(B) = 42`%
`= 0.42`

The probability that does not survive more than 500 temperature cycles and it was manufactured by company A is
`P(A | B' ) = 0.73`

The probability that the computer chip is not manufactured by company A and does not survive more than 500 temperature cycles is mathematically evaluated as

`P(B' n A ' ) = P (B' | A' ) P(B ')`

Where
`B' \ and \ A'` are a A and B complements and | represented AND operator

So

`P(B' n A ' ) = [1 - P (B' | A )] [1 - P(B )]`

substituting values

`P(B' n A ' ) = [1 - 0.73] [1 - 0.42 ]`

`P(B' n A ' ) = (0.27 )(0.58)`

`P(B' n A ' ) =0.16`

`P(B' n A ' ) =` 16%