| Sum $S$ | Probability of $S$: $P(S)$ | Net Gain/Loss (in dollars) $G$ | Product $G\cdot P(S)$ |
| 2 | $\dfrac{1}{36}$ | 5 | $\dfrac{5}{36}$ |
| 3 | $\dfrac{1}{18}$ | 5 | $\dfrac{5}{18}$ |
| Sum $S$ | Probability of $S$: $P(S)$ | Net Gain/Loss (in dollars) $G$ | Product $G\cdot P(S)$ |
| 2 | $\dfrac{1}{36}$ | 5 | $\dfrac{5}{36}$ |
| 3 | $\dfrac{1}{18}$ | 5 | $\dfrac{5}{18}$ |
| 4 | $\dfrac{1}{12}$ | 5 | $\dfrac{5}{12}$ |
| 5 | $\dfrac{1}{9}$ | -5 | $-\dfrac{5}{9}$ |
| 6 | $\dfrac{5}{36}$ | -5 | $-\dfrac{25}{36}$ |
| 7 | $\dfrac{1}{6}$ | -5 | $-\dfrac{5}{6}$ |
| 8 | $\dfrac{5}{36}$ | -5 | $-\dfrac{25}{36}$ |
| 9 | $\dfrac{1}{9}$ | -5 | $-\dfrac{5}{9}$ |
| 10 | $\dfrac{1}{12}$ | 5 | $\dfrac{5}{12}$ |
| 11 | $\dfrac{1}{18}$ | 5 | $\dfrac{5}{18}$ |
| 12 | $\dfrac{1}{36}$ | 5 | $\dfrac{5}{36}$ |
The expected value in probability is a measure of the average outcome of a random variable. It is calculated by multiplying each possible outcome by its probability and then summing all of these values together.
Expected value is used in decision making as a way to quantify the potential gains or losses of a certain action. It helps individuals or businesses make informed decisions by considering all possible outcomes and their corresponding probabilities.
Yes, expected value can be negative. This means that the potential outcome of a certain action has a higher probability of resulting in a loss rather than a gain. It is important to consider the expected value when making decisions, as it takes into account both the potential gains and losses.
Sample size does not directly affect the expected value, but it can affect the accuracy of the expected value. With a larger sample size, the expected value will be a more accurate representation of the true average outcome. However, even with a small sample size, the expected value can still provide valuable insights.
Expected value is a calculated measure based on the probabilities of possible outcomes, while actual value is the real outcome that occurs. Expected value helps us make decisions by considering all potential outcomes, while actual value reflects the specific outcome that has occurred.