Question

It’s been said that if you put a billion monkeys in front of a billion typewriters for a billion years, they will eventually type the complete works of Shakespeare. Let’s consider this. Suppose that our billion monkeys have keyboards with just capital letters, three punctuation symbols and a space bar, and that each is typed with equal probability. (Continuing below)

Answer 1

Now suppose that each monkey can type twelve characters per second, and that putting paper into and taking paper out of a typewriter takes no time. How long would it take before the probability that one of our monkeys typed TO BE OR NOT alone on a single sheet of paper exceeded 50%? Assume they have been trained to insert a page, type 12 (random) characters, and remove the page. For this problem, you may wish to use the approximation (1 + x)^n ≈ e^nx ≈ 1 + nx, valid for small x, positive or negative.