Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $9. If you roll a 3, 4 or 5, you win $2. Otherwise, you pay $3.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 X P(X) b. Find the expected profit. $ (Round to the nearest cent)c. Interpret the expected value. You will win this much if you play a game. If you play many games, on average, you will likely win, or lose if negative, close to this amount. This is the most likely amount of money you will win. d. Based on the expected value, should you play this game? No, this is a gambling game and it is always a bad idea to gamble. Yes, because you can win $9.00 which is greater than the $3.00 that you can lose. No, since the expected value is negative, you would be very likely to come home with less money if you played many games. 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.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $9. If you roll a 3, 4 or 5, you win $2. Otherwise, you pay $3.
a. Complete the
Probability Distribution Table
| X | P(X) |
|---|---|
b. Find the expected profit. $ (Round to the nearest cent)
c. Interpret the
- You will win this much if you play a game.
- If you play many games, on average, you will likely win, or lose if negative, close to this amount.
- This is the most likely amount of money you will win.
d. Based on the expected value, should you play this game?
- No, this is a gambling game and it is always a bad idea to gamble.
- Yes, because you can win $9.00 which is greater than the $3.00 that you can lose.
- No, since the expected value is negative, you would be very likely to come home with less money if you played many games.
- 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.
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