Understanding the expected value in probability is crucial for decision-making in various fields such as finance, statistics, and gaming. The expected value represents the average outcome of a random variable over many trials.

**Formula:** The formula for calculating the expected value (EV) is given by:

��=�(�)×�+(1−�(�))×�*E**V*=*P*(*S*)×*X*+(1−*P*(*S*))×*Y*

Where:

- �(�)
*P*(*S*) is the probability of success, - �
*X*is the value of success, and - �
*Y*is the value of failure.

**How to Use:**

- Enter the probability of success (P(S)).
- Input the value of success (X).
- Specify the value of failure (Y).
- Click the “Calculate” button.

**Example:** Suppose you have a 70% chance (0.7) of winning $100 (X) and a 30% chance (0.3) of losing $50 (Y).

**FAQs:**

*What is the expected value in probability?*- The expected value is the average outcome of a random variable over multiple trials.

*How is the expected value calculated?*- The formula is ��=�(�)×�+(1−�(�))×�
*E**V*=*P*(*S*)×*X*+(1−*P*(*S*))×*Y*, where P(S) is the probability of success.

- The formula is ��=�(�)×�+(1−�(�))×�
*Why is the expected value important?*- It helps in decision-making by providing an average outcome to anticipate.

*Can the expected value be negative?*- Yes, it can be negative if the potential losses outweigh the gains.

*Is the expected value guaranteed to occur?*- No, it is a theoretical average and may not represent any specific outcome in a single trial.

**Conclusion:** Calculating the expected value probability is a valuable tool in decision theory. This calculator simplifies the process, allowing users to make informed decisions based on probabilities and potential outcomes. Consider using this tool in scenarios involving risk and reward to enhance decision-making processes.