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Consider the roll of a pair of standard dice. Let X be the random variable that represents the sum of the two dice. By the fundamental counting principle, because rolling each die has 6 possible outcomes, the number of all possible results is 6⋅6=36. Additionally, the possible values of X are integers from 2 to 12.
A table that represents the theoretical probability distribution of X will now be created. Frequencies represent the number of dice roll results that add up to the given values x of the random variable X. The frequency is divided by 36 to determine the theoretical probability of each outcome.
X=Sum of Two Dice | ||
---|---|---|
x | Frequency | P(X=x) |
2 | 1 | 361≈0.028 |
3 | 2 | 362≈0.056 |
4 | 3 | 363≈0.083 |
5 | 4 | 364≈0.111 |
6 | 5 | 365≈0.139 |
7 | 6 | 366≈0.167 |
8 | 5 | 365≈0.139 |
9 | 4 | 364≈0.111 |
10 | 3 | 363≈0.083 |
11 | 2 | 362≈0.056 |
12 | 1 | 361≈0.028 |