## PROBABILITY CALCULATIONS

We have now studied all the rules of probability for discrete events: the axioms of probability and conditional probability and the definition of independence. The following are examples of calculating probabilities using these rules.

EXAMPLE 2.5.1 Using the axioms of conditional probability, we shall solve the same problem that appears in Example 2.3.4. In the present approach we recognize only two types of cards, aces and nonaces, without paying any attention to the other characteristics—suits or numbers. We shall first compute the probability that three aces turn up in a particular sequence: for example, suppose the first three cards are aces and the last two nonaces. Let A* denote the event that the ith card is an ace and let TV, denote the event that the ith card is a nonace...

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