Problem 17.2. (a) What's the probability that 0 doesn't appear among & digits chosen independently and uniformly at random? (b) A box contains 90 good and 10 defective screws. What's the probability that if we pick 10 screws from the box, none will be defective? (c) First one digit is chosen uniformly at random from {1, 2, 3, 4,5} and is re- moved from the set; then a second digit is chosen uniformly at random from the remaining digits. What is the probability that an odd digit is picked the second time? (d) Suppose that you randomly permute the digits 1, 2, . .. , n, that is, you select a permutation uniformly at random. What is the probability the digit & ends up in the ith position after the permutation? (e) A fair coin is flipped n times. What's the probability that all the heads occur at the end of the sequence? (If no heads occur, then "all the heads are at the end of the sequence" is vacuously true.)