Complete the following probability distribution table: Probability Distribution Table X P(X) - 13 0. 1 50 0.4 57 59 0.4Suppose that you are offered the following I'deal." You roll a six sided die. If you roll a 6, you win $115. If you roll a 3, 4 or 5, you win 54. Otherwise, you pay $9. a. Complete the PDF Table. List the K values, where X is the profit, from smallest to largest. Round to 4 decimal places where appropriate. Probability Distribution Table b. Find the expected profit. 5| [Round to the nearest cent] c. Interpret the expected value. '32:! You will win this much if you play a game. CL" This is the most likely amount of money you will win. '32? If you play many games you will likely win on average very close to 51.6? per game. d. Based on the expected value, should you play this game? (:3 No, this is a gambling game and it is always a bad idea to gamble. '12:? Yes, since the expected value is D, you would be very likely to come very close to breaking even if you played many games, so you might as well have fun at no cost. Ci'Yes, because you can win $16.00 which is greater than the $9.00 that you can lose. '33:? Yes, since the expected value is positive, you would be very likely to come home with more money if you played many games. '3' No, since the expected value is negative, you would be very likely to come home with less money if you played many games. 60.13 of all violent felons in the prison system are repeat offenders. If 315 violent felons are randomly.r selected, find the probability...r that a. Exa-ztlyr 21 of them are repeat offenders. I I b. At most 20 of them are repeat offenders. I I c. At least 21 of them are repeat offenders. I I d. Between 20 and 24 {including it] and 24] of them are repeat offenders. T113 of allAmericans live in cities with population greater than 100,000 people. If 33 Americans are randomly.' selected, find the probability.r that a. Exactly 21 of them Live in cities with population greater than 100,000 people. I I b. At most 26 of them live in cities with population greater than 100,000 people. I I c. At least 23 of them live in cities with population greater than 100,000 people. I I d. Between 18 and 24 {including 18 and 24] of them live in cities with population greater than 100,000 people. 15 cards are selected Out of a 51 card deck such that after each card is selected, it is placed back into the deck and the deck is reshuffled. Then the total number of hearts selected follows a binomial distribution. '12:? false '12:? true 200 randomly selected Americans are asked if they smoke cigarettes. Then the results of this procedure can be treated as a binomial distribution. '3:_:3' false '33-:3' true 7