For example, if a fair 6-sided die is rolled, the expected value of the number rolled is 3.5. 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.

## 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 is the expected value of the maximum of rolling 2 dice?

Therefore, the expected value of the max is (1 + 2*3 + 3*5 + 4*7 + 5*9 + 6*11) / 36 = **161/36**.

## How do you find the expected value of a dice?

The expected value of the random variable is (in some sense) its average value. You compute it by **multiplying each value x of the random variable by the probability P(X=x)**, and then adding up the results. So the average sum of dice is: E(X) = 2 ^{.} 1/36 + 3 ^{.} 2/36 + ….

## How many times do you have to roll a dice to get a 6?

Ok, let’s translate this into a simple question about rolling a die: How many times would you expect to roll a die to see a 6? The probability of getting a six in a single throw is 1/6. Therefore, on average, you’ll have **about six throws for every appearance of a 6**.

## How many sums can you get from rolling 2 dice?

Note that there are **36 possibilities for** (a,b). This total number of possibilities can be obtained from the multiplication principle: there are 6 possibilities for a, and for each outcome for a, there are 6 possibilities for b. So, the total number of joint outcomes (a,b) is 6 times 6 which is 36.

## What is the expectation of getting 5 on a roll of a dice?

Two (6-sided) dice roll probability table

Roll a… | Probability |
---|---|

4 | 3/36 (8.333%) |

5 | 4/36 (11.111%) |

6 | 5/36 (13.889%) |

7 | 6/36 (16.667%) |

## What is 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.

## What is the variance of rolling two dice?

Rolling two dice, should give a variance of 22Var(one die)=**4×3512≈11.67**.

## What is the mean of a dice roll?

The mean is the type of average most people are used to. To find the mean **for a set of numbers, add the numbers together and divide by the number of numbers in the set**. For example, if you roll two dice thirteen times and get 9, 4, 7, 6, 11, 9, 10, 7, 9, 7, 11, 5, and 4, add the numbers to produce a sum of 99.

## What is the probability of getting a 7 when rolling 2 dice?

Probabilities for the two dice

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

4 | 3 | 8.33% |

5 | 4 | 11.11% |

6 | 5 | 13.89% |

7 | 6 |
16.67% |

## When two sided dice are rolled There are 36 possible outcomes?

Every time you add an additional die, the number of possible outcomes is multiplied by 6: 2 dice 36, 3 dice 36*6 = **216 possible outcomes**.