In probability, an expected value is the probability of each and every event in a sample space times the probability that the event will occur.^{[1]} Since the expected value is numeric, the outcomes of the experiment must also be numeric. For experiments with finite outcomes, this can be calculated as the sum of the values of each outcome times the probability of that outcome occurring.
Table 1 shows the outcomes and their probabilities for the roll of one fair die.
Outcome of roll | Probability | Outcome × Probability |
---|---|---|
1 | ||
2 | ||
3 | ||
4 | ||
5 | ||
6 | ||
Table 1: Expected value of role of one fair die |
So, the expected value is .
Table 2 shows the outcomes and their probabilities for the roll of two fair dice.
Outcome of roll | Probability | Outcome × Probability |
---|---|---|
2 | ||
3 | ||
4 | ||
5 | ||
6 | ||
7 | ||
8 | ||
9 | ||
10 | ||
11 | ||
12 | ||
Table 2: Expected value of role of two fair dice |
So, the expected value is .
# | A | B | C | D |
E | F | G | H | I |
J | K | L | M | N |
O | P | Q | R | S |
T | U | V | W | X |
Y | Z |
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