Q 1. The card game of Euchre employs a deck that consists of all four of each of the aces, kings, queens, jacks, tens, and nines (one of each suit—clubs, diamonds, spades, and hearts). (a) Find the probability that a randomly selected card from a Euchre deck is a jack (J). (Enter the fraction without reduction on the left hand side of "=" symbol and the final answer on the right hand side reduced to the lowest possible fraction.) (b) Find the probability that a randomly selected card from a Euchre deck is a spade (S). (Enter the fraction without reduction on the left hand side of "=" symbol and the final answer on the right hand side reduced to the lowest possible fraction.) (c) Find the probability that a randomly selected card from a Euchre deck is a jack or an ace (A). (Enter the fraction reduced to the lowest possible fraction on the left hand side of "=" symbol and the final answer on the right hand side simplified to the lowest possible fraction. Leave no cells blank - be certain to enter "0" wherever required.) (d) Find the probability that a randomly selected card from a Euchre deck is a jack or a spade. (Enter the fraction reduced to the lowest possible fraction on the left hand side of "=" symbol and the final answer on the right hand side simplified to the lowest possible fraction.) (e) Are the events J and A mutually exclusive? J and S? Why or why not? 2. Each month a brokerage house studies various companies and rates each company’s stock as being either “low risk” or “moderate to high risk.” In a recent report, the brokerage house summarized its findings about 61 aerospace companies and 42 food retailers in the following table: Company Type Low Risk Moderate to High Risk Aerospace company 46 15 Food retailer 18 24 ________________________________________ If we randomly select one of the total of 103 companies (a) Find the probability that the company's stock is moderate to high risk given that the firm is an aerospace company. (Round your answer to 4 decimal places.) (b) Find the probability that the company's stock is moderate to high risk given that the firm is a food retailer. (Round your answer to 4 decimal places.) (c) Determine if the company type is independent of the level of risk of the firm's stock. (Round your answers to 4 decimal places.) 3. How many combinations of three high-risk stocks could you randomly select from eight high-risk stocks? What is the probability that you would obtain the three highest-returning stocks? (Round your answer to 4 decimal places.) 4. 40 percent of all customers who enter a store will make a purchase. Suppose that 6 customers enter the store and that these customers make independent purchase decisions. (1) Use the binomial formula to calculate the probability that exactly five customers make a purchase. (Round your answer to 4 decimal places.) (2) Use the binomial formula to calculate the probability that at least three customers make a purchase. (Round your answer to 4 decimal places.) (3) Use the binomial formula to calculate the probability that two or fewer customers make a purchase. (Round your answer to 4 decimal places.) (4) Use the binomial formula to calculate the probability that at least one customer makes a purchase. (Round your answer to 4 decimal places.)