Question

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?

Answer 1

0.1566

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%.