Question 1. A fair coin is tossed three times. The outcomes of the three tosses are recorded. (a) List all 8 outcomes in the sample space. (b) Assuming the outcomes to be equally likely, find the probability that all three tosses are Heads. (c) Assuming the outcomes to be equally likely, find the probability that all three tosses are the same. (d) Assuming the outcomes to be equally likely, find the probability that exactly one of the three tosses is Heads. Question 2. A sample of 20 cars is selected from the inventory of a dealership. Let A: At least 3 of the cars in the sample are red, and let B: Fewer than 2 of the cars in the sample are red. Determine whether A and B are mutually exclusive.| Question 3. The following table presents the average annual energy expenditures (in dollars) for housing units of various sizes (in square feet) Data for Question 3 Size 250 750 1250 1750 750 2250 2750 3250 3750 Energy Exp. 1087 1228 1583 1798 3000 1939 2138 2172 2315 (a) Use software to compute the least-squares regression line for predicting energy consumption from house size, and the coefficient of determination. (b) Construct and sketch a scatterplot (a lot of details are not necessary). Which point is an outlier? (c) Is the outlier influential? Explain. (d) Remove the outlier, and recompute both the least-squares regression and the coefficient of determination (e) Construct and sketch a residual plot. Does the relationship appear to be linear? Question 4 In a certain state, license plates consist of four digits from 0 to 9 followed by three letters. Assume the numbers and letters are chosen at random. Replicates are allowed. How many different license plates can be formed? Show work that backs up your answer to receive credit. No partial credit given.