The Probability of a Random Number
A number n is chosen at random from the set {1, 2, ..., 20}. We are interested in k, the integer power of 2 which exactly divides n. Recall that we say that 2k exactly divides n if 2^k|n but 2^(k+1) |/ n. We write "a||b" for "a exactly divides b".

a) Set up a probability space to model this experiment.

b) Define k formally as a random variable. (What kind of thing is a random variable?)

c) Find the range of k.

d) Find the sets "k = i" for every i in the range of k.

e) Find the probability function of k.

f) Find the expected value of k.