P(non conforming bottle) = P(non conforming | machine A) * P(machine A) + P(non conforming | machine B) * P(machine B)

assuming it is equally likely to have either machine:

P(non conforming bottle) = 0.01 * 0.5 + 0.025 * 0.5 = 0.0175

——

P(machine A) = 1/2

——–

P(machine B and conforming) = P(conforming | B) * P(B)

= 0.025 * 0.5 = 0.0125

———

P(machine A OR conforming)

= P(machine A) + P(conforming) – P(machine A and conforming)

= 1/2 + 0.9825 – 0.99 * 0.5

= 0.9875

What is the probability that a bottle selected is a non-conforming bottle?

3.5 out of 200 or 1.75%

What is the probability that a bottle selected was produced on machine A? 100 out of 200 or 50%

What is the probability that a bottle selected was filled on machine B and is a conforming bottle?

97.5 out of 200 or roughly 48%

What is the probability that a bottle selected was filled on machine A or is a conforming bottle?

99 out of 200. or roughly 49.5 %