Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $15. If you roll a 4 or 5, you win $5. Otherwise, you pay $9. **Question: Based on the expected value, should you play this game?**- 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. - Yes, since the expected value is positive, you would be very likely to come home with more money if you played many games. - Yes, because you can win $15.00 which is greater than the $9.00 that you can lose. - No, this is a gambling game and it is always a bad idea to gamble. - No, since the expected value is negative, you would be very likely to come home with less money if you played many games. ### Educational Content: Probability and Expected Value#### Scenario:You are offered a "deal" where you roll a six-sided die:- If you roll a 6, you win $15.- If you roll a 4 or 5, you win $5.- Otherwise, you pay $9.#### Tasks:**a. Complete the Probability Distribution Table:**List the X values, where X represents the profit, from smallest to largest. Round to four decimal places where appropriate.| X (Profit) | P(X) (Probability) ||------------|---------------------|| | || | || | |**b. Calculate the Expected Profit:**Find the expected profit and round to the nearest cent. Expected Profit: $ ________**c. Interpret the Expected Value:**Choose the correct interpretation of the expected value:- [ ] If you play many games, you will likely lose on average very close to $0.33 per game.- [ ] You will win this much if you play a game.- [ ] This is the most likely amount of money you will win.#### Explanation:To complete the table, calculate the probability for each outcome:- Rolling a 6 (profit: $15): Probability = 1/6.- Rolling a 4 or 5 (profit: $5): Probability = 2/6.- Rolling any other number, i.e., 1, 2, 3 (loss: -$9): Probability = 3/6.Next, calculate the expected profit by considering all possible outcomes and their probabilities. For each outcome, multiply the profit by its probability and sum these products to get the expected value.

Name: Suppose that you are offered the following "deal." You roll a six side
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $15. If you roll a 4 or 5, you win $5. Otherwise, you pay $9. **Question: Based on the expected value, should you play this game?**- Yes, since the