A certain threecylinder combination lock has 75 numbers on it. To open it, you turn to a number on the first cylinder, then to a second number on the second cylinder, and then to a third number on the third cylinder and so on until a three-number lock combination has been effected. Repetitions are allowed, and any of the 7'5 numbers can be used at each step to form the combination. (a) How many different look combinations are there? (b) What is the probability of guessing a lock combination on the rst try? '1) (a) The number of different threenumber lock combinations is 421,875 . (Type an integer or fraction. Simplify your answer.) 1 (b) The probability that the correct lock combination is guessed on the first try is I. (Type an integer or fraction. Simplify your answer.) In a certain game of chance, a wheel consists of 44 slots numbered 00, 0, 1, 2 ..... 42. To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. Complete parts (a) through (c) below. E) Hm \""'l-" ovaw ID 1W!- V The sample space is {00, 0, 1. 2..... 42}. The sample space is {00, 0}. The sample space is {1, 2,..., 42}. (b) Determine the probability that the metal ball falls into the slot marked 3. Interpret this probability. The probability that the metal ball falls into the slot marked 3 is 0.0227 . (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and ll in the answer box within your choice. (Type a whole number.) v If the wheel is spun 1000 times. it is expected that about 23 of those times result in the ball landing in slot 3. If the wheel is spun 1000 times, it is expected that exactly of those times result in the ball not landing in slot 3. (0) Determine the probability that the metal ball lands in an odd slot. Interpret this probability. The probability that the metal ball lands in an odd slot is El. (Round to four decimal places as needed.)