In this video, we are going to learn about the differences between theoretical probability and experimental probability.

Let’s use rolling a dice as an example. Use *P* to represent probability.

**Theoretical:** The ratio of possible ways that an event can happen to the total number of outcomes.

Theoretically, the probability of rolling a even number on a dice ranging from *1* to *6* would be , or simply just .

To roll a one, the theoretical probability would be .

On a larger scale, it also means that theoretically, the probability

of rolling one number is the same.

**Experimental:** The ratio of the number of times an event happens to the total number of outcomes.

Let’s use the following table to find the experimental probability after rolling a dice *60* times.

Outcome | Frequency |

1 | 15 |

2 | 18 |

3 | 7 |

4 | 20 |

5 | 2 |

6 | 8 |

Experimentally, the probability of rolling a even number would be the sum of the frequency for even outcomes to the total number of trials.

, or simply just

To roll a one, the experimental probability would be .

Note that the probability of rolling each number is different, as well as when compared to the theoretical probabilities.

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