## Expected Probability

### In probability theory, the expected probability refers to the average probability of an event occurring

In probability theory, the expected probability refers to the average probability of an event occurring. It is also known as the expected value or the mean of a random variable. The expected probability can be calculated by multiplying each possible outcome by its corresponding probability and summing them up.

Let’s illustrate this with an example. Suppose we have a fair six-sided die, and we want to find the expected probability of rolling a number greater than 3. We can start by listing the possible outcomes and their probabilities:

Outcome 4: Probability = 1/6

Outcome 5: Probability = 1/6

Outcome 6: Probability = 1/6

To calculate the expected probability, we multiply each outcome by its probability, and then sum them up:

Expected Probability = (4 × 1/6) + (5 × 1/6) + (6 × 1/6)

= (4/6) + (5/6) + (6/6)

= 15/6

= 2.5

So, the expected probability of rolling a number greater than 3 is 2.5. This means that if we were to repeat the experiment many times, we can expect to roll a number greater than 3 approximately 2.5 times on average.

The concept of expected probability is widely used in various areas of mathematics and statistics, including decision-making, risk analysis, and forecasting. It helps us make informed predictions and understand the likelihood of different outcomes.

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