The American roulette
wheel has 38 slots numbered 00, 0, and 1-36. Slots 00 and 0 are green. Half of
the slots numbered 1-36 are red and half are black. The experiment consists of
rolling a ball in a groove in the wheel; the ball eventually falls randomly
into one of the 38 slots. The roulette wheel is shown in the left graph panel;
the ball is shown on each update.

One of seven different bets can be selected from the list box: On each update, the outcome X is shown graphically in the first panel and recorded numerically in the first table. Random variable W gives the net winnings for the chosen bet; this variable is recorded in the first table on each update. The density function and moments of W are shown in blue in the distribution graph and are recorded in the distribution table. On each update, the empirical density and moments of W are shown in red in the distribution graph and are recorded in the distribution table.

One of seven different bets can be selected from the list box: On each update, the outcome X is shown graphically in the first panel and recorded numerically in the first table. Random variable W gives the net winnings for the chosen bet; this variable is recorded in the first table on each update. The density function and moments of W are shown in blue in the distribution graph and are recorded in the distribution table. On each update, the empirical density and moments of W are shown in red in the distribution graph and are recorded in the distribution table.

- Bet on 1. This is an example of a straight bet, a bet on a single number. The bet pays 35:1.
- Bet on 1, 2. This is an example of a split bet, a bet on 2 numbers. The bet pays 17:1
- Bet on 1, 2, 3. This is an example of a row bet, a bet on 3 numbers. The bet pays 11:1.
- Bet on 1, 2, 4, 5. This is an example of 4-number bet, and pays 8:1.
- Bet on 1-6. This is an example of a 2-row bet, a bet on 6 numbers. The bet pays 5:1.
- Bet on 1-12. This is an example of a 12-number bet, and pays 2:1.
- Bet on 1-18. This is an example of an 18-number bet, and pays 1:1.

## Software/Applets used on this page

an applet from PSOL from UAH

## Glossary

### density

the ratio of the mass of an object to its volume

### function

A rule that connects one value in one set with one and only one value in another set.

### graph

A diagram showing a relationship between two variables.

The diagram shows a vertical y axis and a horizontal x axis.

The diagram shows a vertical y axis and a horizontal x axis.

### random variable

a variable that represents the values obtained when measurements are taken from a population in the real world; it must take a numerical value.

### straight

The type of line produced by a linear equation.

### variable

A value which is unknown and free to vary, often denoted by x or y.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|

AQA A-Level (UK - Pre-2017) | S1 | Probability | Experimental | - |

AQA AS Maths 2017 | Statistics | Probability | Experimental Probabilities | - |

AQA AS/A2 Maths 2017 | Statistics | Probability | Experimental Probabilities | - |

CBSE XII (India) | Probability | Probability | Repeated independent (Bernoulli) trials and binomial distribution | - |

CBSE XI (India) | Statistics and Probability | Probability | Random experiments, outcomes, sample spaces (set representation) | - |

CCEA A-Level (NI) | S1 | Probability | Experimental | - |

CIE A-Level (UK) | S1 | Probability | Experimental | - |

Edexcel A-Level (UK - Pre-2017) | S1 | Probability | Experimental | - |

Edexcel AS Maths 2017 | Statistics | Probability | Experimental Probabilities | - |

Edexcel AS/A2 Maths 2017 | Statistics | Probability | Experimental Probabilities | - |

I.B. Higher Level | 5 | Probability | Experimental | - |

I.B. Standard Level | 5 | Probability | Experimental | - |

Methods (UK) | M15 | Probability | Experimental | - |

I.B. (MSSL) | 3 | Probability | Experimental | - |

OCR A-Level (UK - Pre-2017) | S1 | Probability | Experimental | - |

OCR AS Maths 2017 | Statistics | Probability | Experimental Probabilities | - |

OCR MEI AS Maths 2017 | Statistics | Probability | Experimental Probabilities | - |

OCR-MEI A-Level (UK - Pre-2017) | S1 | Probability | Experimental | - |

Pre-Calculus (US) | E4 | Probability | Experimental | - |

Pre-U A-Level (UK) | Prob | Probability | Experimental | - |

Scottish (Highers + Advanced) | HS | Probability | Experimental | - |

Scottish Highers | S | Probability | Experimental | - |

Universal (all site questions) | P | Probability | Experimental | - |

WJEC A-Level (Wales) | S1 | Probability | Experimental | - |