What is the expected value in probability?

The expected value in probability is a fundamental concept that quantifies the average outcome of a random variable when considering all possible values it can take, each weighted by its likelihood of occurrence. This means that rather than just taking a straightforward average of observed values, the expected value incorporates the probabilities associated with each potential outcome.

When calculating the expected value, you multiply each possible value by the probability of that value occurring and then sum all these products. This approach allows for a more comprehensive understanding of a variable's behavior over repeated trials or events, making it particularly useful in fields such as finance, insurance, and various scientific disciplines.

The other choices reflect different statistical concepts: the mode refers to the most frequently occurring value in a dataset, the median indicates the middle value when a dataset is ordered, and the highest value simply denotes the maximum value observed. None of these definitions capture the concept of weighting values by their associated probabilities, which is central to the definition of expected value.