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Probability COMPOUND EVENTS

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If two sets or events have no elements in common, they are called disjoint or mutually exclusive. Examples of mutually exclusive sets: Two fair dice are tossed, what is the probability of a sum of 7 or 11? A card is randomly selected from a standard deck of cards. What is the probability that it is a 10 OR a face card? If A and B are disjoint events, then the probability of A OR B is: P( A or B) = P(A ) + P(B)

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Examples of mutually exclusive sets: Two fair dice are tossed, what is the probability of a sum of 7 or 11?

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Examples of mutually exclusive sets: A card is randomly selected from a standard deck of cards. What is the probability that it is a 10 OR a face card?

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Examples of mutually exclusive sets: In this last situation there is no overlap: 10

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But if I changed the question to: A card is randomly selected from a standard deck of cards. What is the probability that it is a 10 OR a heart?

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So we need to modify our formula and subtract out that overlap so we don’t count it twice: This is called a COMPOUND EVENT.

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Two sets are INDEPENDENT if the occurrence of one has NO EFFECT on the occurrence of the other. Examples of independent: Two fair dice are tossed, what is the probability of a sum of 12? A computer generates three random numbers…. P( A and B) = P(A ) ∙ P(B) NOTICE: There is no “ or”. Compound events ask for probability of this “ or” that. If there is overlap we are also able to find a this “and” that”.

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Out of 200 students 113 are either varsity athletes or on the honor roll. There are 74 students who are varsity athletes and 51 who are on the honor roll. What is the probability that a randomly selected senior is both a varsity athlete AND on the honor roll?

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