# What is the expected value of rolling 3 dice?

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Expected value of one die is 1/6*(1+2+3+4+5+6)=3.5. Expected value of three dice is 3*3.5=10.5.

## What is the expected sum of three dice?

There are 216 possible outcomes when three dice are thrown. Since the dice are ‘fair’ each of them has an equal probability. There are 27 different combinations that produce a sum of 10 (1–3–6, 2–2–6, etc).

## What is the probability of rolling 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 rolling a sum of 4?

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%

## What is the expected value of rolling 2 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 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.

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## How do you find the expected value and variance?

The expected value µ = E(X) is a measure of location or central tendency. The standard deviation σ is a measure of the spread or scale. The variance σ2 = Var(X) is the square of the standard deviation. To move from discrete to continuous, we will simply replace the sums in the formulas by integrals.

## How do you calculate expected profit?

Subtract the total cost from the gross income to determine the expected profit. If your cost of goods sold is \$200 for 100 pieces and your total expenses applied to that product are \$400 for the month, then the overall cost of your item to you is \$600. 