12.4 Probability of Compound Events

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Presentation transcript:

12.4 Probability of Compound Events

If A and B are two events, then the probability of A or B is: P(A or B) = P(A) + P(B) – P(A and B) If A and B are mutually exclusive, then the probability of A or B is: P(A or B) = P(A) + P(B) Mutually Exclusive Events-A and B are mutually exclusive if the intersection between A and B is empty.

Probability of Mutually Exclusive Events Solution: Let event A be selecting an ace, and let even B be selecting a face card. Event A has 4 outcomes and event B has 12 outcomes. Because A and B are mutually exclusive, the probability is: Example 1: A card is randomly selected from a standard deck of 52 cards. What is the probability that it is an ace of a face card? P(A or B) = P(A) + P(B) = 4/52 + 12/52 =16/52 = 4/13 = 0.308

Probability of a compound event Example 2: A card is randomly selected from a standard deck of 52 cards. What is the probability that the card is a face or a face card?

Probability of a Compound Event 4 9 3 8 2 7 10 K Q J K Q J K Q J Solution: Let event A be selecting a heart, and let event B be selecting a face card. Event A has 13 outcomes and event B has 12 outcomes. Of these, three outcomes are common to A and B. So, the probability of selecting a heart or a face card is: P(A or B) = P(A) +P(B) – P(A and B) = 13/52 + 12/52 -3/52 =22/52 =11/26 =0.423