Multiple event probability refers to the probability of two or more events occurring simultaneously or in sequence. The probability of multiple events occurring can be calculated using the multiplication rule, which states that the probability of two or more independent events occurring together is equal to the product of their individual probabilities.

For example, consider the probability of rolling a 1 on a fair 6-sided die and then flipping a coin and getting heads. The probability of rolling a 1 is 1/6, and the probability of getting heads on a coin flip is 1/2. The probability of both events occurring together is:

P(rolling a 1 and getting heads) = P(rolling a 1) x P(getting heads) = (1/6) x (1/2) = 1/12

Similarly, the probability of three or more events occurring together can be calculated by multiplying the probabilities of each individual event.

Probability

In mathematics, probability is a measure of the likelihood of an event occurring. It is a branch of mathematics concerned with the study of random events, outcomes, and experiments. Probability theory provides a formal framework for analyzing situations where there is uncertainty, such as gambling, insurance, and finance, as well as many other areas of science and engineering.

The probability of an event is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur. For example, the probability of flipping a coin and getting heads is 0.5, or 50%, assuming the coin is fair.

There are two main approaches to probability: classical (or theoretical) probability and empirical (or experimental) probability. Classical probability is based on mathematical principles and assumes that all outcomes are equally likely. Empirical probability, on the other hand, is based on observations and experiments, and involves collecting data to estimate the probability of an event.

Probability is used in a variety of mathematical fields, including statistics, combinatorics, and calculus, as well as in applications such as gambling, finance, and risk management.