Problem # 1 (20). A three-digit number (000 to 999) is chosen at random (i.e., each possible number is equally likely to be chosen). First, find the probability of each event specified in parts (a)-(d): a) (4) The number is greater than 399 b) (4) The product of the last two digits is 6 c) (4) Exactly two digits are greater than 8 d) (4) The second digit is greater than the other two e) (4) Next, let Ak be the event that the chosen number is less than or equal to integer k, for 0 k 999, and let B be the event that the chosen number is even. For what values of k are Ak and B independent?