The probability of the sum of three dice being 16 is zero. The largest possible sum with three dice is 18 (6 + 6 + 6), so the sum of 16 is not achievable.

The probability of the sum of three dice being 16 is indeed zero. When three dice are thrown simultaneously, the maximum possible sum is 18 (when all dice show a 6). Since the sum of 16 is lower than the maximum achievable sum, it is not possible to obtain this specific sum.

To understand why the sum of 16 cannot be achieved, let’s consider all the possible combinations of dice rolls and their corresponding sums:

Dice 1 | Dice 2 | Dice 3 | Sum |
---|---|---|---|

1 | 1 | 1 | 3 |

1 | 1 | 2 | 4 |

1 | 1 | 3 | 5 |

1 | 1 | 4 | 6 |

1 | 1 | 5 | 7 |

1 | 1 | 6 | 8 |

1 | 2 | 1 | 4 |

1 | 2 | 2 | 5 |

1 | 2 | 3 | 6 |

1 | 2 | 4 | 7 |

1 | 2 | 5 | 8 |

1 | 2 | 6 | 9 |

6 | 6 | 5 | 17 |

6 | 6 | 6 | 18 |

As seen in the table, there are no combinations that result in a sum of 16. Each cell represents a unique outcome of the dice roll, and it is evident that the sum of 16 is not present in the entire set of possible outcomes.

To further emphasize the impossibility of obtaining a sum of 16, consider the following quote by Albert Einstein, who was known for his mathematical prowess: “Insanity: doing the same thing over and over again and expecting different results.” In this case, rolling the three dice repeatedly will never yield a sum of 16 because it is simply not a possible outcome.

Interesting facts about dice rolling:

- The standard dice used in most board games have six sides, numbered from 1 to 6.
- Dice have been used for thousands of years, with the oldest known dice dating back over 5,000 years.
- Dice games are prevalent in many cultures and have been used for both entertainment and divination purposes.
- The probability of rolling a specific number on a fair six-sided die is 1 in 6, as each outcome is equally likely.
- Dice are often used in probability and statistics to simulate random events and calculate odds.

In summary, the probability of the sum of three dice being 16 is zero because it is not a possible outcome given the maximum sum achievable with three dice being 18. This understanding can be supported by analyzing all the possible combinations of dice rolls. As Albert Einstein once said, expecting different results from repeating the same action is simply not rational.

**You might discover the answer to “When three dice are thrown simultaneously then find the probability that sum of the digits is 16?” in this video**

In this video, the speaker discusses the frequencies and probabilities when three dice are tossed. They explain the pattern of frequencies for different sums and calculate the frequencies for each sum. They also explain how to calculate the probabilities by dividing the favorable number of cases by the total number of outcomes. The speaker provides examples of different probabilities for various totals and discusses the probability of getting a total of at least 6 or a total between 9 and 12. They also explain how to calculate the probability of getting a total of at least 14. Overall, the video provides a comprehensive overview of the frequencies and probabilities when three dice are tossed.

**Other responses to your inquiry**

Probability of a sum of 16: 6/216 = 2.8%

2.8%Probability of a sum of 16: 6/216 =

2.8%

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