Probability and Statistics

Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 and 1.

Theoretical probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes.

The probability of an event not occurring is calculated as 1 minus the probability of the event occurring.

A sample space is the set of all possible outcomes of a probability experiment.

Independent events are those whose outcomes do not affect each other, while dependent events are those where the outcome of one event affects the outcome of another.

To find the probability of multiple independent events occurring, multiply the probabilities of each individual event.

A random variable is a variable whose possible values are numerical outcomes of a random phenomenon.

The expected value is the long-term average or mean of a random variable, calculated as the sum of all possible values, each multiplied by its probability.

Discrete random variables can take on a countable number of values, while continuous random variables can take on an infinite number of values within a given range.

A probability distribution describes how the probabilities are distributed over the values of the random variable.