Suppose that a small chest contains three drawers. The first drawer contains two $1 bills, and the second drawer contains one $1 bill and one $100 bill. These bills are enclosed in identical envelopes. Suppose that first a drawer is selected at random and then one of the two bills inside that drawer is selected at random. We can define these events;

A = the first drawer is selected, B = the second drawer is selected,

C = a $1 bill is selected

1. Suppose when you randomly select one drawer and then one bill from that drawer, the bill you obtain is a $1 bill. What is P(B | C), the probability that the second bill in this drawer is a $100 bill? Answer this question intuitively without making any calculations.
2. Use the relative frequency concept of probability to estimate P(B | C) as follows. First select a drawer by flipping a coin once. If head, the first drawer is selected and you know that both A and C has occurred. If tail, the second drawer is selected: flip the coin a second time and if you get a head, this will indicate that you have selected the envelope with $1, in other words B and C has occurred. If you get a tail for the second flip, then C has not occurred. Repeat this process 50 times. How many times in these 50 repetitions did the event C occur? What proportion of the time did B occur when C occurred? Use this proportion to estimate P(B | C). Does this estimate support your guess of P(B | C) in part a?
3. Calculate P(B | C) using the procedures developed in this chapter (a tree diagram may be helpful). Was your estimate in part b close to this value? Explain.