Suppose that you are offered the following deal You roll a six sided die If you roll a 6 you win 14 If you roll a 3 4 or 5 you win 2 Otherwise you pay 6 a Complete the PDF Table List the X values where X is the profit from smallest to largest Round to 4 decimal places where appropriate Probability Distribution P X X Table b Find the expected profit Round to the nearest cent c Interpret the expected value O You will win this much if you play a game O If you play many games you will likely win on average very close to 1 33 per game O This is the most likely amount of money you will win d Based on the expected value should you play this game O Yes since the expected value is positive you would be very likely to come home with more money if you played many games O Yes because you can win 14 00 which is greater than the 6 00 that you can lose O No since the expected value is negative you would be very likely to come home with less money if you played many games O No this is a gambling game and it is always a bad idea to gamble O Yes since the expected value is 0 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