Question

Half of a set of the parts are manufactured by machine A and half by machine B. Ten percent of all the parts are defective. Six percent of the parts manufactured on machine A are defective. Find the probability that a part was manufactured on machine A, given that the part is defective. (Round your answer to 4 decimal places.) Probability

Answer 1

The probability that a part was manufactured on machine A is 0.3

Explanation:

Consider the provided information.

It is given that Half of a set of parts are manufactured by machine A and half by machine B.

P(A)=0.5

Let d represents the probability that part is defective.

Ten percent of all the parts are defective.

P(d) = 0.10

Six percent of the parts manufactured on machine A are defective.

P(d|A)=0.06

Now we need to find the probability that a part was manufactured on machine A, and given that the part is defective :

`P(A|d) =(P(A \cap d))/(P(d))`

`P(A|d) =(P(d|A)* P(A))/(P(d))\\P(A|d)= (0.06* 0.5)/(0.10)`

`P(A|d)= 0.3`

Hence, the probability that a part was manufactured on machine A is 0.3