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10 April, 19:46

n 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. What is the probability that a computer chip is not manufactured by company A and does not survive more than 500 temperature cycles?

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  1. 10 April, 19:49
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    0.1566

    Step-by-step explanation:

    We are given that probability of survival of computer chip for more than 500 temperature is

    P (S) = 0.42

    Also, we are given that if the computer chips not survives then it was made by company A. So,

    P (A/S') = 0.73

    We have to find the probability of computer chips not survives and not made by company A i. e. P (A'∩S') = ?

    P (A/S') can be written as

    P (A/S') = P (A∩S') / P (S')

    where P (S') = 1-P (S) = 1-0.42=0.58

    and P (A∩S') = P (A) - P (A∩S)

    P (A/S') = P (A) - P (A∩S) / 0.58

    0.73*0.58=P (A) - P (A∩S)

    P (A) - P (A∩S) = 0.4234

    P (A'∩S') = 1-P (A∪S) = 1-[P (S) + P (A) - P (A∩S) ]=1-[0.42+0.42340]=0.1566

    Thus, the probability of computer chips not survives and not made by company A is 15.66%.
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