Answer:
The probability that a part was manufactured on machine A is 0.3
Step-by-step 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 :
[tex]P(A|d) =\frac{P(A \cap d)}{P(d)}[/tex]
[tex]P(A|d) =\frac{P(d|A)\times P(A)}{P(d)}\\P(A|d)= \frac{0.06\times 0.5}{0.10}[/tex]
[tex]P(A|d)= 0.3[/tex]
Hence, the probability that a part was manufactured on machine A is 0.3
