5) please make sure your answer is correct, Thank You So Much!

Question 5 (9 points) Suppose there is a carnival gan'ie where you select 1 marble out of a bag of 40 marbles. Inside the bag there is 1 Blue Marble, 2 Red Marbles, 3 Green Marbles and 34 White Marbles. The payouts for the game are as follows: Draw a Blue Marble: Win 10 dollars Draw a Red Marble: Win 5 dollars Draw a Green Marble: Win 3 dollars Draw a White Marble: Lose 1 dollar (a) Construct a probability model for this game. (1)) Calculate the probability that you WIN money on any one. play of the game. (e) Calculate the probability that you LOSE money on 15 plays of this game in a row. ((1) Calculate the expected value for this game. Interpret this value. Is this a good or bad game? (e) Suppose that after (30 plays of this game you have lost a total of 23 dollars. Is this better or worse than predicted by the expected value? (f) What should drawing a Blue Marble pay for this game to be fair? Extra Credit Question 2) (2 points) Look back at Question 5. Suppose you play this game 7 times. What is the probability that after 7 plays you have lost money? (Hint: You'll have lost money if you have lost all 7 times OR if you have lost 6 times and won the 3 dollar prize once OR if you have lost 6 times and won the 5 dollar prize once. Otherwise, you'll have won money)