Probabilities of unions and intersections

Def. The union (in Russian textbooks given as the sum) of several events is the event that occurs if at least one of these events occurs on a single performance of the experiment. The union is denoted by the symbol (if we have two events A and B then the union will be denoted as following ).

Def. The intersection (in Russian textbooks given as the product) of several events is the event that occurs if all these events occur on a single performance of the experiment. The intersection is denoted by the symbol (if we have two events A and B then the intersection will be denoted by symbol ).

The additive rule of probability: Probability of a union of several events can be calculated by using formula

Def. Events are called mutually exclusive (взаимоисключающими или несовместными) if any two of them cannot be realized simultaneously.

Theorem. If events are mutually exclusive then

Def. The probability of the event A that is calculated as we suppose that the event B has occurred is called the conditional probability and we write .

The multiplicative rule of probability: Probability of an intersection of several events can be calculated by using formula

Def. Events are independent events if the occurrence of some of them does not alter the probabilities that the rest of them have occurred.

If events are independent events then the last formula can be rewritten

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