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

Answer:

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

Step-by-step 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%