How many possible outcomes are there if you roll a 12 sided die?
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How many possible outcomes are there if you roll a 12 sided die?
You can use the Fundamental Counting Principal to find the total possible outcomes. For each roll of the 12 sided die you can have 20 pairings with the other one. Therefore, you can have 12 X 20 or 240 possible outcomes.
What is the expected value of a roll of a fair die?
3.5
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 rolling a 12 on a 12 sided die?
Two (6-sided) dice roll probability table
| Roll a… | Probability |
|---|---|
| 9 | 30/36 (83.333\%) |
| 10 | 33/36 (91.667\%) |
| 11 | 35/36 (97.222\%) |
| 12 | 36/36 (100\%) |
How do you find the expected value of a roll of 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.
How do you find the probability of a 12 sided die?
12-sided die The probability of any number being rolled can be written as 1 in 12 or 1⁄12. We can also calculate the percentage chance using 1 ÷ 12 × 100 (remember you always do division before multiplication). So you have a 8.33\% chance of rolling a 1, 8.33\% chance of rolling a 2, etc.
What is the expected value of the roll of two 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.
What is a fair dice roll?
In mathematics we say “fair dice” when we mean that there is an equally likely chance of landing on any face. Because the faces are all the same, there is an equal chance of landing on any face. So, using the platonic solids we can have dice with 4, 6, 8, 12 or 20 faces!
Is rolling a dice fair?
At its simplest, a fair die means that each of the faces has the same probability of landing facing up. A standard six-sided die, for example, can be considered “fair” if each of the faces has a probability of 1/6.
How do you find the expected value?
How to find the expected value?
- Multiply each random value by its probability of occurring.
- Sum all the products from Step 1.
- The result is the expected value.
When rolling a 12 sided die What is the probability of rolling an even number or a multiple of 3?
Explanation: The probability of rolling a 3 is 16 . The probability of rolling an even number is 36 .
What is the sample space of a fair 12 sided dice?
The possible outcomes for rolling a 12 sided die once (assuming the die has values 1–12) is presented below in the sample space S: S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
What is the probability of rolling a 12 sided die?
The expected value of a dice roll is 6.5 for a standard 12-sided die (a die with each of the numbers 1 through 12 appearing on exactly one face of the die). In this case, for a fair die with 12 sides, the probability of each outcome is the same: 1/12. The possible outcomes are the numbers 1 through 12: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
How many sides does a fair die have?
Consider the fair die is 6 sided If you’ve used dice a lot, you may have noticed that the pips on opposite sides always add up to 7.
What is the expected value of a single die roll?
The expected value of a single die roll is 3.5, assuming a fair 6-sided die (the numbers 1 through 6 are printed on the sides and appear exactly once each, and the probability of each outcome is 1/6). Remember that the expected value of an action is a weighted average of each possible outcome.
What is the expected value of a single six-sided die?
If you’ve used dice a lot, you may have noticed that the pips on opposite sides always add up to 7. Since this is the same for all three pairs of opposite sides and each pair has the same chance of being rolled and both sides of each pair have the same chance of being rolled, the expected value of a single six-sided die is 7 / 2.