Question 5. Consider a scenario in which a random integer is chosen from the range 1000 to 9999 (inclusive). (a) Assuming a uniform distribution, what is the probability that the number will have distinct digits? (b) Assuming a uniform distribution, what is the probability that the number will be a multiple of 2 or a multiple of 3? (0) Assuming a uniform distribution, what is the probability that the number will not be a multiple of 10? (d) Assuming a uniform distribution, what is the probability that the number will not be a multiple of 5 or of 7? Question 6. Consider a scenario in which Alice, Bob, and Carl are playing a game that consists of 7 rounds. In each round, there are no draws and only one winner. The probability of Alice winning a round is 0.43. The probability of Bob winning a round is 0.37. The probability of Carl winning a round is 0.2. (a) What is the probability that Alice wins exactly 4 rounds? (b) What is the probability that one of the players wins all 7 rounds? (c) What is the probability that Alice wins three rounds, Bob wins 3 rounds, and Carl wins 1 round? ((1) What is the probability that Alice wins at least 5 rounds given that she wins the rst two rounds? Are these two events independent? Explain your answer. (e) What is the probability that Alice does not win any games given that Carl wins the rst round and Bob wins rounds 2 and 3. Are these events independent? Explain your