Best answer: What is the expected value of product of points on n dice?

What is the expected value of sum of points on n dice?

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.

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 expected output of a dice?

Each die has six sides, and so there are six possible outcomes for each die when rolled individually. However, when rolled together, there are 6 * 6 = 36 possible outcomes!

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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 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 expected value in probability?

The expected value (EV) is an anticipated value for an investment at some point in the future. 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.

How do I find the expected value of a game?

In general, to find the expected value for a game or other scenario, find the sum of all possible outcomes, each multiplied by the probability of its occurrence.

What are all the possible outcomes of 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.

When a dice is rolled the six possible outcomes are?

The set of all the possible outcomes is called the sample space. Thus the numbers on the die become the set. The sample space has six possible outcomes: {1, 2, 3, 4, 5, 6}.

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What is the probability of rolling a 2 with 2 dice?

Probabilities for the two dice

Total Number of combinations Probability
2 1 2.78%
3 2 5.56%
4 3 8.33%
5 4 11.11%