# How do you calculate the probability of compound events?

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.

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.

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To calculate the probability of compound events, you typically use the multiplication rule or the addition rule, depending on whether the events are independent or dependent. For independent events, you multiply the probabilities of each event occurring. For dependent events, you may need to use conditional probability or the addition rule, which involves adding the probabilities of the individual events and subtracting the probability of their intersection if they are mutually exclusive.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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