Consider a game in which you roll a die and receive $1 for each spot that occurs. (a) What are the expected winnings from this game? (b) If you paid $4 to play this game, how much would you lose, on average, each time you played the game?
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.
Consider a game in which you roll a die and receive $1 for each spot that occurs.
(a) What are the expected winnings from this game?
(b) If you paid $4 to play this game, how much would you lose, on average, each time you played the game?
Given that we receive $1 for each spot that occurs. This means we receive the amount same as the number appeared.
We make a probability distribution table using the given information.
| outcome | 1 | 2 | 3 | 4 | 5 | 6 |
| winning amount | 1 | 2 | 3 | 4 | 5 | 6 |
| probability |
so the expected winning is:
Answer(a): $3.5
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