In the game of Rusisian roulette, one inserts a single cartridge into he drum of a revolver, leaving the other five chambers of the drum empty. One then spins the drum, aims at one's head, and pulls the trigger.
(1)What is the probability of being still alive after playing the game N times ?
(2)What is the probability of surviving (N-1) turns in this game and then being shot the Nth time one pulls the trigger?
(3)What is the mean number of times a player gets the opportunity of pulling the trigger in this macabre game?
Assume that typographical errors committed by a typesetter occur completely at random. Suppose that a book of 600 pages contain 600 such errors. Use Poisson distribution to calculate the probability.
(1)That a page contain no errors.
(2)That a page contains at least three errors.