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The die coin experiment consists of rolling a die and then tossing a coin the number of times shown on the die. The die score N and the number of heads X are recorded on each update. The density function and moments of X are shown in the blue in the second graph and are recorded in the second table. On each update, the empirical density and moments of X are shown in red in the second graph and are recorded in the second table. The probability of heads p for the coin can be varied with a scroll bar, and any of the following die distributions can be chosen from the list box:
  • fair: each face has probability 1/6
  • 1-6 flat: faces 1 and 6 have probability 1/4 each; faces 2, 3, 4, and 5 have probability 1/8 each.
  • 2-5 flat: faces 2 and 5 have probability 1/4 each; faces 1, 3, 4, and 6 have probability 1/8 each.
  • 3-4 flat: faces 3 and 4 have probability 1/4 each; faces 1, 2, 5, and 6 have probability 1/8 each.
  • skewed left: face i has probability i / 21 for i = 1, 2, 3, 4, 5, 6.
  • skewed right: face i has probability (7 - i) / 21 for i = 1, 2, 3, 4, 5, 6.

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.

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-