07) In an automated filling operation, the probabilities of an incorrect fill when the process is operated at a low speed,
medium speed, and high speed are 0.01, 0.05, and 0.1 respectively. Assume that 50% of containers are filled at
low speed, 30% of containers are filled at medium speed, and 20% of containers are filled at high speed.
(a) What is the total probability of incorrect filling?
[5 Points]
(b) When a random container is examined, what is the probability that it would've been filled at a low speed,
given that, the container had an incorrect fill volume?
[5 Points]
(c) When a random container is examined, what is the probability that it would've been filled at a medium
speed, given that, the container had an incorrect fill volume?
[5 Points]
(d) When a random container is examined, what is the probability that it would've been filled at a high speed,
given that, the container had an incorrect fill volume?
[5 Points]
(e) Comparing your answers to (b), (c), and (d), explain which speed category (low, medium or high) causes
the largest proportion of incorrect fillings.
[5 Points]