# How do you calculate the probability of compound events?

##### 1 Answer

*Compound events* are combinations of *elementary events*. For example, when rolling a dice, an *elementary event* is any concrete result of a single rolling - a number on top from 1 to 6. An example of a *compound event* is an event of having rolled two dice getting 6 on each.

A *compound event* can consist of *independent elementary events*. This is the case when the result of any one *elementary event* does not have any influence on the result of another. An example with two dice above is such a *compounded event*.

Alternatively, we might have a situation of *elementary events* that depend on each other. For example, a *compounded event* of having a sum of two numbers rolled on two dice being less than 6.

In case of *independent elementary events* that are composed into a *compounded event*, the probability of a *compounded event* equals to a product of probabilities of its *elementary* parts. Thus, the probability of having rolled two 6 with two dice equals to a product of probability of having 6 on the first dice (that is,

More complex case of probability of a *compounded event* that consists of *dependent elementary events* requires the knowledge of *conditional probabilities* and equals to a product of probability of one event by a *conditional probability* of another under condition that the first *elementary event* has occurred.

More detailed analysis of *events*, *probabilities*, *conditional probabilities* and other concept can be found in the chapter *Probability* at Unizor - free on-line course of advanced mathematics for teenagers.