The game of American Roulette consists of spinning a wheel in one direction and then spinning a small ball in the other direction, see videoOpens externally [+]. The ball will eventually fall into a slot of the wheel. The wheel is divided into 38 slots. There are 36 slots numbered from 1 through 36 and 2 slots which are labeled with zero "0" and double zero "00". The zero and double zero are colored green, 18 slots are colored red, and the other 18 are colored black. See the below picture. A common bet in the game is to bet on red or black which pays even money. For example, if you bet a $1.00 on red and the ball falls into a red slot, then you win $1.00. Otherwise, you lose $1.00. Suppose you play the game and you bet $6 on red. Let X = the amount you win. a.) Complete the probability distribution table. (Write answers as fractions.) X P(X) -6 6 b.) Find the expected value (mean) of X. μμ = (Write you answer as fraction or round to two decimal places.) c.) Find the standard deviation of X. σσ = (Round your answer to two decimal places.)
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.
The game of American Roulette consists of spinning a wheel in one direction and then spinning a small ball in the other direction, see videoOpens externally [+]. The ball will eventually fall into a slot of the wheel. The wheel is divided into 38 slots. There are 36 slots numbered from 1 through 36 and 2 slots which are labeled with zero "0" and double zero "00". The zero and double zero are colored green, 18 slots are colored red, and the other 18 are colored black. See the below picture.
A common bet in the game is to bet on red or black which pays even money. For example, if you bet a $1.00 on red and the ball falls into a red slot, then you win $1.00. Otherwise, you lose $1.00. Suppose you play the game and you bet $6 on red. Let X = the amount you win.
a.) Complete the
| X | P(X) |
|---|---|
| -6 | |
| 6 |
b.) Find the
μμ = (Write you answer as fraction or round to two decimal places.)
c.) Find the standard deviation of X.
σσ = (Round your answer to two decimal places.)
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