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scZoUnD [109]
3 years ago
5

In a reliability test there is a 42% probability that a computer chip survives more than 500 temperature cycles. If a computer c

hip 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?
Mathematics
1 answer:
Strike441 [17]3 years ago
7 0

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%

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