Enter the probability of an event occurring and the number of trials into the calculator to determine the expected value.

Expected Value Formula

The following formula is used to calculate an expected value.

EV = P(x) * n
  • Where EV is the expected value of the expected number of successes
  • P(x) is the probability of event x occurring
  • n is the number of trials

To calculate the expected value, multiply the probability of the event occurring by the number of trials.

Expected Value Definition

An expected value is the sum of the probability of an event occurring and the number of trials performed.

Expected Value Example

How to calculate an expected value?

  1. First, determine the probability of the event happening.

    This will be the probability of a given value, or the probability or a given even. For this example we will say there is a 25% chance of an event occurring.

  2. Next, determine the number of trials.

    For this example we will say there will be 100 trials.

  3. Finally, calculate the expected value.

    Calculate the expected number of events given the 25% chance and the 100 trials, so 100*.25 = 25 total expected.


What does the expected value tell you in practical terms?
The expected value provides a measure of the central tendency or average outcome of a random event based on its probabilities. It helps in predicting the long-term average outcome of repeated experiments or trials.

How can expected value be applied in decision-making?
Expected value can be crucial in financial, business, and personal decision-making processes. It allows individuals and organizations to evaluate the potential benefits and risks of different options, helping them to choose the one with the best expected outcome.

Is the expected value always accurate in predicting outcomes?
While the expected value offers a theoretical average of outcomes based on probability, actual results can vary, especially in a small number of trials. Over a large number of trials, the outcomes tend to converge towards the expected value, making it more accurate in predicting long-term results.