The likelihood that an event will occur is measured by probability and is quantified as a number between 0 (impossibility) and 1 (certainty).
The expected value of an experiment is the probability-weighted average of all possible values. An important concept here is the law of large numbers which states that the average result from a series of trials will converge to the expected value.
One of the main goals of statistics is to estimate unknown parameters. An estimator uses measurements and properties of expectation to approximate these parameters. Estimation theory is a very important concept in Statistics as usually we have data for the sample and not for the population.