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## What is the expected sum of numbers that appear when 3 fair dice are rolled?

E(S) = E(s1+s2+s3) = E(s1)+E(s2)+E(s3). The expectation of the sum is the sum of the expectation values for the three dice. But since they are all fair dice, they have the same expectation values. Hence **E(S) = 3 E(s1)**.

## 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 + ….

## What is the expected value of 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 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 a sum of 3 If a dice is thrown?

probability of getting sum as 3 = **1/18**

When two dice are thrown together, the probability of getting a …

## What is the expected value of the sum of the numbers that appear when a pair of fair dice is rolled?

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.

## What is the sample space of rolling 3 dice?

When three dice are rolled sample space contains **6 × 6 × 6 = 216 events** in form of triplet (a, b, c), where a, b, c each can take values from 1 to 6 independently. Therefore, the number of samples is 216.

## 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 value of dice?

Mathwords: Expected Value. **A quantity equal to the average result of an experiment after a large number of trials**. For example, if a fair 6-sided die is rolled, the expected value of the number rolled is 3.5. This is a correct interpretation even though it is impossible to roll a 3.5 on a 6-sided die.

## What is the expected payout of the game?

The payoff of a game **is the expected value of the game minus the cost**. If you expect to win about $2.20 on average if you play a game repeatedly and it costs only $2 to play, then the expected payoff is $0.20 per game.