Problem A. In a small clock repair shop, there are three clocksmiths: clocksmith A, clocksmith B, and clocksmith C. Suppose that
clocksmith A takes on 50% of the jobs, clocksmith B takes on 30% of the jobs, and clocksmith C takes on 20% of the jobs. Being the most
skilled of the three, only 5% of clocksmith A's repairs fail, whereas 15% of clocksmith B's repairs fail and 25% of clocksmith C's repairs
fail. Suppose an item was just submitted for repair.
Question A.0. Draw a clearly labeled tree diagram that represents this situation, including probabilities.
Question A.1. What is the probability that the item will be successfully repaired (that is, not fail)?
Enter your answer here, rounded to 4 decimal places: 0.6667
Question A.2. What is the probability that a successfully repaired item was repaired by clocksmith C?
Enter your answer here, rounded to 4 decimal places:
Problem B. Consider a training program where 3% of its participants drop out. If a team of 11 people participate in the program, what is
the probability that at least one of them ends up dropping out of the training? Assume that each participant drops out of the program
independent of each other.
Enter your answer here:
