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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.
  • 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



the ratio of the mass of an object to its volume


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


A diagram showing a relationship between two variables.
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.


The type of line produced by a linear equation.


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

Full Glossary List

This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AQA A-Level (UK - Pre-2017)S1ProbabilityExperimental-
AQA AS Maths 2017StatisticsProbabilityExperimental Probabilities-
AQA AS/A2 Maths 2017StatisticsProbabilityExperimental Probabilities-
CBSE XII (India)ProbabilityProbabilityRepeated independent (Bernoulli) trials and binomial distribution-
CBSE XI (India)Statistics and ProbabilityProbabilityRandom experiments, outcomes, sample spaces (set representation)-
CCEA A-Level (NI)S1ProbabilityExperimental-
CIE A-Level (UK)S1ProbabilityExperimental-
Edexcel A-Level (UK - Pre-2017)S1ProbabilityExperimental-
Edexcel AS Maths 2017StatisticsProbabilityExperimental Probabilities-
Edexcel AS/A2 Maths 2017StatisticsProbabilityExperimental Probabilities-
I.B. Higher Level5ProbabilityExperimental-
I.B. Standard Level5ProbabilityExperimental-
Methods (UK)M15ProbabilityExperimental-
I.B. (MSSL)3ProbabilityExperimental-
OCR A-Level (UK - Pre-2017)S1ProbabilityExperimental-
OCR AS Maths 2017StatisticsProbabilityExperimental Probabilities-
OCR MEI AS Maths 2017StatisticsProbabilityExperimental Probabilities-
OCR-MEI A-Level (UK - Pre-2017)S1ProbabilityExperimental-
Pre-Calculus (US)E4ProbabilityExperimental-
Pre-U A-Level (UK)ProbProbabilityExperimental-
Scottish (Highers + Advanced)HSProbabilityExperimental-
Scottish HighersSProbabilityExperimental-
Universal (all site questions)PProbabilityExperimental-
WJEC A-Level (Wales)S1ProbabilityExperimental-