You draw one card at random from a standard deck of 52...

You draw one card at random from a standard deck of
52 playing cards. Find the probability that (a) the card is an even-numbered card, (b) the card is a heart or a diamond, and (c) the card is a nine or a face card.
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Key Concepts

Mutually Exclusive Events

Mutually exclusive events are events that cannot occur at the same time. Recognizing whether events are mutually exclusive is important in probability theory because it determines how probabilities should be combined, especially when using rules like the addition rule.

Addition Rule for Probabilities

The addition rule is a principle used to determine the probability of the occurrence of at least one of several events by summing the probabilities of the individual events. It is particularly useful when dealing with mutually exclusive events, although adjustments are needed if the events are not mutually exclusive.

Counting Methods

Counting methods involve combinatorial techniques such as the basic counting principle, permutations, and combinations, which are used to enumerate the number of ways an event can occur. These methods are critical in determining the number of favorable outcomes when calculating probabilities.

Sample Space

The sample space is the complete set of all possible outcomes of a random experiment. In probability problems, correctly identifying the sample space is essential because it defines the context within which events and their probabilities are evaluated.

Probability

Probability is the branch of mathematics that measures the likelihood of an event occurring by comparing the number of favorable outcomes to the total number of possible outcomes. It is foundational for reasoning about uncertainty and risk in various contexts, including games of chance, statistics, and real-world scenarios.

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