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## What is the sum of all the numbers on a dice?

The most common type of die is a six-sided cube with the numbers 1-6 placed on the faces. The value of the roll is indicated by the number of “spots” showing on the top. For the six-sided die, opposite faces are arranged to always sum to **seven**.

## What is the expected value of rolling a dice?

When you roll a fair die you have an equal chance of getting each of the six numbers 1 to 6. The expected value of your die roll, however, is **3.5**.

## What must be the expected sum of the scores on the two dice?

The expectation of the sum of two (independent) dice is the sum of expectations of each die, which is **3.5 + 3.5 = 7**. Similarly, for N dice throws, the expectation of the sum should be N * 3.5. If you’re taking only the maximum value of the two dice throws, then your answer 4.47 is correct.

## How do you calculate the expected value?

In statistics and probability analysis, the expected value is calculated **by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values**. By calculating expected values, investors can choose the scenario most likely to give the desired outcome.

## What is the probability of 3 dice?

Two (6-sided) dice roll probability table

Roll a… | Probability |
---|---|

3 | 3/36 (8.333%) |

4 | 6/36 (16.667%) |

5 | 10/36 (27.778%) |

6 | 15/36 (41.667%) |

## What is the probability of getting at most the sum of 3 in casting a pair of dice?

There are no other combinations that sum to 3, so we have 2 out of a total of 36 combinations that sum to 3. Therefore, the answer is 2/36 = **1/18**.

## What is the probability of sum of two dice?

Probabilities for the two dice

Total | Number of combinations | Probability |
---|---|---|

10 | 3 | 8.33% |

11 | 2 | 5.56% |

12 | 1 | 2.78% |

Total | 36 |
100% |

## How do you calculate expected sum?

The expected value of the sum of several random variables is equal to the sum of their expectations, e.g., **E[X+Y] = E[X]+ E[Y]** . On the other hand, the expected value of the product of two random variables is not necessarily the product of the expected values.