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

## 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.

## 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 | - |