(a) Three typed letters and their envelopes are piled on a desk. If someone puts the letters into the envelopes at random (one letter in each), what is the probability that each letter gets into its own envelope? Call the envelopes A, B, C, and the corresponding letters a, b, c, and set up the sample space. Note that ``a in C, b in B, c in A'' is one point in the sample space.
(b) What is the probability that at least one letter gets into its own envelope? Hint: What is the probability that no letter gets into its own envelope?
(c) Let A mean that a got into envelope A, and so on. Find the probability P(A) that a got into A. Find P(B) and P(C). Find the probability P(A+B) that either a or b or both got into their correct envelopes, and the probability P(AB) that both got into their correct envelopes. Verify equation (3.6).