Assume that the probability of a “success” on a single experiment with n outcomes is 1/n. Let m be the number of experiments necessary to make it a favourable bet that at least one success will occur (see Exercise 1.1.5). (a) Show that the probability that, in m trials, there are no successes is (1 − 1/n) m.
(b) (de Moivre) Show that if m = n log 2 then
(c) Would De Moivre have been led to the correct answer for de Mere’s two bets if he had used his approximation?