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Venn Diagrams and Set Operations: Tools for Probability

Properties of the Probability of an Event. Here are some properties of the probability of an event that everyone must remember. Let E be an event of a sample space S.If E is the empty set, then P(E)=0. For instance, if two dice are tossed, the probability that the sum of the faces that turn up

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Venn Diagrams and Set Operations: Tools for Probability

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    1. Venn Diagrams and Set Operations: Tools for Probability

    2. Properties of the Probability of an Event Here are some properties of the probability of an event that everyone must remember. Let E be an event of a sample space S. If E is the empty set, then P(E)=0. For instance, if two dice are tossed, the probability that the sum of the faces that turn up is less than 2 is 0. If E is the whole sample space S, then P(E)=1. For instance, if two dice are tossed, the probability that the sum of the faces that turn up is between 2 and 12, inclusive, is 1. Otherwise, 0<P(E)<1. That is, the probability of an event is always positive and is never more than 1.

    3. Sets and Venn diagrams can help us investigate other interesting properties of the probability of an event.

    4. Example #1 12,000 people voted for a politician in his first election, 15,000 voted for him in his second, and 3,000 voted for him in both elections. 55,000 people voted in the elections. What is the probability that a randomly chosen voter voted for the politician in at least 1 one of the elections? in neither one of the elections?

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