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Question 1: Introduction to Probability The number of cars a dealer sells daily was recorded over the last 200 days. The data are summarised as follows: Daily sales # of cars sold (frequency) 0 10 30 2 70 3 50 4 40 A. Complete the probability distribution table below. i.e. Daily sales P(daily sales) 0 1 2 3 4 Total B. What is the probability that the company will sell 3 cars on a given day? ANSWER: C. What is the probability that the company will sell 4 cars on a given day? ANSWER: D. What is the probability that the company will sell 3 or more cars on a given day? ANSWER:Question 2: Finding Probabilities of Events The number of spots turning up when a 6-sided die is tossed is observed. The list of possible outcomes or sample space is S = {1, 2, 3, 4, 5, 6} Consider the following events: E: The number observed is an even number. i.c. E={,2,4,6} F: The number observed is at most 2 i.c. F={1,2} Answer the following CASES ANSWER a. Find P(E). i.c. Probability of an event: What is that probability that the outcome will be an even number? ANSWER: b. Find E" and P(E ). i.c. Probability of the complement of an event: (i) list element of Es , and (ii) find is that probability that the outcome will NOT be an even number ? ANSWER: c. Find i.e. Joint probability: What is that probability that the outcome will be (i) an P(E and F) =P(E n F). even number and (ii) at most 2.? ANSWER: d. Find i.c. Union of events: What is that probability that the outcome will be (i) an P(E or F) =P(E U F). even number or (ii) at most 2 or both?? ANSWER: e. Find i.c. Conditional probability: What is that probability that the outcome will P(F given F) =P(F E). be at most 2, given that it is an even number? ANSWER: f. Are events E and F ANSWER: mutually exclusive