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

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## 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 outcomes are there in a roll of 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 theoretical mean for rolling a die?

Use P to represent probability. Theoretical: The ratio of possible ways that an event can happen to the total number of outcomes. Theoretically, the probability of rolling an even number on a dice ranging from 1 to 6 would be , or simply just .

## 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%)
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## What is the expected value of 2 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 find the mean of rolling a dice?

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 theoretical probability that you will roll any number on the dice?

Since there are six possible outcomes, the probability of obtaining any side of the die is 1/6. The probability of rolling a 1 is 1/6, the probability of rolling a 2 is 1/6, and so on.