Question

The probability thay a certain manufacturing process will produce a defective automobile tire is 0.001 the probability that an inspector will reject a defective tire is 0.98 however, the probability that an inspector will incorrectly reject a good tirr is 0.01

A)what is the probability that an inspector will reject a randomly selected tire. State answer four decimal places

B)if an inspector rejects a randomly selected tire,what is the probability that the tire is actually defective? State answer three decimals places

Note: need answer on a paper

Answer 1

a) X =reject the tire

A = not defective

B = defective

P(X) = P(X|A)P(A) + P(X|B)P(B)

= (1- 0.001)* 0.01 +0.001*0.98

= 0.01097

b)

P(B|X) = P(B and X)/P(X)

= 0.001 * 0.98/ 0.01097

= 0.08933