In a certain process, three types of parts are manufactured: Type A, Type B, and Type C. The line processes 80% type A pieces, 12% type B pieces and the rest is type C pieces. parts go through an inspection station in which an automated system is used Of vision. If the system detects that the part does not comply with the specified, it removes it automatically off the line. For this system to be effective, the piece must be properly aligned. If a good part is not positioned correctly within the inspection machine, the system will identify it as defective and reject it, even if it's good. If the part is aligned correctly, the machine ALWAYS takes the correct decision (if it is good it classifies it as good and if it is defective it rejects it and removes it from the line)

The probability that the part is positioned correctly depends on the type of part:

P (correct alignment / A) = 95%

P (correct alignment / B) = 90%

P (correct alignment / C) = 87%

If it is known that of all type A parts manufactured, 98% meet the specifications, of the type B parts, 94% meet the specifications and the Type C parts, 90% meet the specifications,

a) What is the probability that a type A part will be rejected by the machine? (Remember that the piece will be rejected if it does not meet the specifications or if, even meeting the specifications, its alignment on the machine is not correct)

b) What is the probability that a piece will be rejected?

c) If we randomly select one of the rejected pieces, what is the probability that meet the specifications?

d) If you randomly select a part rejected by the machine, what is the probability that it is type A and meets the specifications?