Powerball is a multistate lottery. The probability distribution below represents the cash prizes of Powerball with their corresponding probabilities. a. Use the fact that () = 1 to find the probability of winning nothing. Round this value to 9 decimal places. (This is the last entry in the second column.) b. If the Grand Prize if $15,000,000, () = 15,000,000 * 0.00000000684 = 0.1026. Fill this into the chart. Calculate () for each of the remaining possible values of x to fill in the missing blanks in the third column. (Round these values to 4 decimal places.) c. Calculate the average amount that a player should expect to win per ticket if he plays many times. Round this value to two decimal places. (This is the sum of the values in the third column.) = () = () = d. Each ticket costs $1. Subtract 1 from your answer to question 3 to determine the average amount the player should expect to win or lose per ticket if he plays many times. (Make sure that you label your answer and indicate whether this is a gain or a loss.) x (Cash Prize, $) P(x) () Grand Prize 0.00000000684 200,000 0.00000028 10,000 0.000001711 100 0.000153996 7 0.004778961 4 0.007881463 3 0.01450116 0 () = () =