Hello friends Summarized! Do you like playing dice? Or maybe you have ever been challenged to guess the result of 3 dice being shaken in a closed container? If yes, then this article is for you. This time I will discuss how to predict the 3 dice that are rolled accurately, using the concepts of probability and mathematics.

## What is Probability?

Probability is the science that studies the likelihood of an event occurring. Probability can be calculated by the formula:

**P(A) = n(A) / n(S)**

Where:

- P(A) is the probability of event A
- n(A) is the number of possible events of A
- n(S) is the number of possible events

Example: If we roll a dice, then there are 6 possible outcomes, namely 1, 2, 3, 4, 5, or 6. So n(S) = 6. If we want to know the probability of getting the number 5, then n(A) = 1, because there is only one possibility of getting the number 5. So P(5) = 1/6.

## How to Guess 3 Rolled Dice?

If we want to guess the outcome of 3 dice being rolled in a closed container, then we have to use the combined probability concept. Joint probability is the probability that two or more events will occur simultaneously. The combined probability can be calculated by the formula:

**P(A and B) = P(A) x P(B | A)**

Where:

- P(A and B) is the probability that events A and B occur simultaneously
- P(A) is the probability of event A
- P(B | A) is the probability of event B if event A had already occurred

Example: If we want to know the probability of getting the numbers 5 and 6 from two dice thrown together, then P(5 and 6) = P(5) x P(6 | 5). We know that P(5) = 1/6, because there is a one in six possibility of getting a 5. Then, P(6 | 5) = 1/5, because if one of the dice has a 5, then there are only five possibility for the other dice. So P(5 and 6) = (1/6) x (1/5) = 1/30.

To guess the outcome of the 3 dice being rolled, we must calculate the combined probabilities of the three events, namely:

**P(A and B and C) = P(A) x P(B | A) x P(C | A and B)**

Where:

- P(A and B and C) is the probability of events A, B and C occurring simultaneously
- P(A) is the probability of event A
- P(B | A) is the probability of event B if event A had already occurred
- P(C | A and B) is the probability of event C if events A and B have already occurred

Example: If we want to know the probability of getting the numbers 4, 5, and 6 from three dice that are rolled together, then P(4 and 5 and 6) = P(4) x P(5 | 4) x P(6 | 4 and 5). We know that P(4) = 1/6, because there is one possibility in six of getting a 4. Then, P(5 | 4) = 1/5, because if one of the dice has a 4, then there are only five possibility for the other dice. Then, P(6 | 4 and 5) = 1/4, because if two dice already have the numbers 4 and 5, then there are only four possibilities for the last die. So P(4 and 5 and 6) = (1/6) x (1/5) x (1/4) = 1/120.

Using this formula, we can calculate the probabilities for each possible outcome of the 3 dice being rolled. Here is a table showing the probabilities for each outcome:

Results | Probability |
---|---|

3 | 1/216 |

4 | 3/216 |

5 | 6/216 |

6 | 10/216 |

7 | 15/216 |

8 | 21/216 |

9 | 25/216 |

10 | 27/216 |

11 | 27/216 |

12 | 25/216 |

13 | 21/216 |

14 | 15/216 |

15 | 10/216 |

16 | 6/216 |

17 | 3/216 |

18 | 1/216 |

From this table, we can see that the most likely result is **10** or **11** , because the probability is the highest, which is **27/216** or about **12.5%** . While the most unlikely result is **3** or **18** , because the probability is the lowest, which is **1/216** or around **0.46%** .

## Conclusion and Closing

That’s how to guess the 3 dice that are rolled accurately, using the concepts of probability and mathematics. By calculating the combined probabilities of three events, we can find the probability of each outcome occurring when the three dice are rolled. Hopefully this article is useful and adds to your insight. If you have questions or feedback, please write in the comments column below. Thank you for reading this article to the end. See you in the next article! 😊

Writer and proudly owner of Diringkas.com!

I like to Staying up-to-date with the latest tech advancements, playing video games, discovering new games, and writing about them.