Your friend rolls an "unusual" six-sided die many times. She reports the probabilities of the possible outcomes are about as follows: Number Rolled: 1 2 3 4 5 6 Probability: 0.20 0.20 0.10 0.10 0.10 (a) Complete the table above by calculating the probability of rolling a 4. (b) Your friend creates the following game using this "unusual" die. You will pay her $2 if she rolls an even number and she will pay you $3 if she rolls an odd number.Use the table from part (a) to fill in the probability model below: Outcome: Roll an even number Roll and odd number Amount: Probability: (c) What is the expected value of this game for you? (d) Is this a fair game, meaning that each of you can expect to win the same amount in the long run? Explain.
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.
Your friend rolls an "unusual" six-sided die many times. She reports the probabilities of the possible outcomes are about as follows:
| Number Rolled: | 1 | 2 | 3 | 4 | 5 | 6 |
| 0.20 | 0.20 | 0.10 | 0.10 | 0.10 |
(a) Complete the table above by calculating the probability of rolling a 4.
(b) Your friend creates the following game using this "unusual" die. You will pay her $2 if she rolls an even number and she will pay you $3 if she rolls an odd number.Use the table from part (a) to fill in the probability model below:
| Outcome: | Roll an even number | Roll and odd number |
| Amount: | ||
| Probability: |
(c) What is the
(d) Is this a fair game, meaning that each of you can expect to win the same amount in the long run? Explain.
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