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Two events are said to be independent if the outcome of one event does not affect the outcome of the other. Their probabilities are independent probabilities. If the events are not independent then they are dependent.
To calculate the probabilities of compound events, you can use the multiplication rule or the addition rule, depending on whether the events are independent or mutually exclusive. The multiplication rule is used when the events are independent, and you multiply the probabilities of the individual events. The addition rule is used when the events are mutually exclusive, and you add the probabilities of the individual events.
If the events are independent then you can multiply the individual probabilities. But if they are not, you have to use conditional probabilities.
You multiply together their individual probabilities.
There is no secret: the procedures are well studied. However, it is important to know whether the events are independent or dependent.