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Consider a binomial distribution with 10 trials What is the expected value of this distribution if the probability of success on a single trial is 0.5?
There is no single formula of probability. The probability of a simple event in a trial is a measure of all outcomes which result in the event, expressed as a proportion of all possible outcomes.If all the outcomes have the same probability then it is the ratio of the number of "favourable" outcomes to the total outcomes. However, the definition based on numbers fails if they are not equi-probable.
A product is the result of multiplying two or more numbers. A single number cannot have a product.
This is quickly solved by trial-and-error. Try multiplying two consecutive integers. If the result it too high, try again with lower numbers. If the result is too low, try again with higher numbers.
The term "theoretical probability" is used in contrast to the term "experimental probability" to describe what the result of some trial or event should be based on math, versus what it actually is, based on running a simulation or actually performing the task. For example, the theoretical probability that a single standard coin flip results in heads is 1/2. The experimental probability in a single flip would be 1 if it returned heads, or 0 if it returned tails, since the experimental probability only counts what actually happened.