Q. 6 (Typing monkeys). A monkey is typing on a typewriter. He hits a sequence of random keys independently and with equal probability. The monkey only uses the 26 letters in the English alphabet (monkeys are not big on punctuation or spacing). a. What is the probability that in the first 6 characters, the monkey types two Bs, three Os, and one N (not necessarily in that order)? b. What is the distribution of the first time the monkey types a Q? How long do we have to wait on average until this happens? It is famously said that a monkey typing randomly on a typewriter will eventually type the text of Shakespeare's Hamlet (without punctuation, it is a monkey after all). The text of Hamlet consists of approximately 130000 letters. c. Show that the monkey will indeed eventually type Hamlet.