Chapter 15.3, Problem 10P

1. 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 probabnility 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, n in b, c in A” is one point in the sample sapce.
2. 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?

Let A mean that a get 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).