Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $6. If you roll a 2, 3, 4 or 5, you win $5. Otherwise, you pay $7. 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 Table P(X) b. Find the expected profit. $ (Round to the nearest cent) c. Interpret the expected value. This is the most likely amount of money you will win. Of you play many games you will likely win on average very close to $3.17 per game. You will win this much if you play a game. d. Based on the expected value, should you play this game? 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 Yes, because you can win $6.00 which is greater than the $7.00 that you can lose. ONo, this is a gambling game and it is always a bad idea to gamble. Yes, since the expected value is positive, you would be very likely to come home with more money if you played many games. OYes, 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. O O O
Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $6. If you roll a 2, 3, 4 or 5, you win $5. Otherwise, you pay $7. 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 Table P(X) b. Find the expected profit. $ (Round to the nearest cent) c. Interpret the expected value. This is the most likely amount of money you will win. Of you play many games you will likely win on average very close to $3.17 per game. You will win this much if you play a game. d. Based on the expected value, should you play this game? 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 Yes, because you can win $6.00 which is greater than the $7.00 that you can lose. ONo, this is a gambling game and it is always a bad idea to gamble. Yes, since the expected value is positive, you would be very likely to come home with more money if you played many games. OYes, 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. O O O
Chapter8: Sequences, Series,and Probability
Section: Chapter Questions
Problem 41CT: On a game show, a contestant is given the digits 3, 4, and 5 to arrange in the proper order to form...
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Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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Transcribed Image Text:Question 3
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Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $6. If you roll
a 2, 3, 4 or 5, you win $5. Otherwise, you pay $7.
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 Table
P(X)
b. Find the expected profit. $
(Round to the nearest cent)
c. Interpret the expected value.
This is the most likely amount of money you will win.
If you play many games you will likely win on average very close to $3.17 per game.
You will win this much if you play a game.
d. Based on the expected value, should you play this game?
O No, since the expected value is negative, you would be very likely to come home with less money if you
played many games.
Yes, because you can win $6.00 which is greater than the $7.00 that you can lose.
No, this is a gambling game and it is always a bad idea to gamble.
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, 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.
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