(Solved): Principle of Statistics Please answer the following questions and attach your work to the submission ...

Please answer the following questions and attach your work to the submission link in Blackboard. An American roulette wheel consists of 38 slots labeled \( 0,00,1,2,3,4, \ldots, 36 \). 18 slots of the American roulette wheel are colored red \( (1,3,5,7,9,12,14,16,18,19 \), \( 21,23,25,27,30,32,34,36) \). 18 slots of the American roulette wheel are colored black \( (2,4,6,8,10,11,13,15,17 \), \( 20,22,24,26,28,29,31,33,35) \) 2 slots of the American roulette wheel are colored green \( (0,00) \). To determine the winning number in a single round of American roulette, the dealer spins the wheel in one direction and spins the ball along a track in the opposite direction. When the ball loses momentum, it falls into one of the 38 slots along the wheel. Consider the probability experiment in which one round of American roulette is played and the winning number is recorded. 1. [2, 2] Should you use the Classical Approach or Empirical Approach to compute probabilities for this probability experiment? Briefly explain the reason for your choice. 2. [3] What is the probability that the ball lands in a red slot? Report your answer as a number between 0 and 1 . Report your answer as a number between 0 and 1 . Round your answer to five decimal places. 3. [3] What is the probability that the ball lands in a green slot? Report your answer as a number between 0 and 1 . Round your answer to five decimal places. 4. [3] What is the probability that the ball lands in an odd numbered slot? Report your answer as a number between 0 and 1 . Round your answer to five decimal places. 5. [2] Briefly explain why the events "ball lands in a red slot" and "ball lands in a green slot" are disjoint. 6. [3] What is the probability that the ball lands in a red slot or in a green slot? Report your answer as a number between 0 and 1 . Round your answer to five decimal places. 7. [2] Briefly explain why the events "ball lands in a red slot" and "ball lands in an odd numbered slot" are not disjoint. 8. [3] What is the probability that the ball lands in a red slot or in an odd numbered slot? Report your answer as a number between 0 and 1 . Round your answer to five decimal places. 9. [2, 2] Are the results of two consecutive rounds of roulette independent? Briefly explain your reasoning. 10. [4] What is the probability that the ball lands in a green slot in two consecutive rounds of roulette? Report your answer as a number between 0 and 1 . Round your answer to five decimal places. 11. [2, 2] Are the results of four consecutive rounds of roulette independent? Briefly explain your reasoning. 12. [4] What is the probability that the ball lands in a red slot in four consecutive rounds of roulette? Report your answer as a number between 0 and 1 . Round your answer to five decimal places.