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?

Question

Mathematics

Maxwell Marquez

12 September, 04:11

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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Noble · Answer 1

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%.