13.2 Complements and Unions of Events Understand the relationship between the probability of an event and the probability of its complement. Calculate the probability of the union of two events. Use complement and union formulas to compute the probability of an event.

We can compute the probability of an event by finding the probability of its complement. Computing the probability of the complement of an event-If E is an event, then P(E`) = 1 – P(E). If 23.7% of a group of people do not have a party affiliation, then the probability of selecting a person from this group that does have a party affiliation is 0.763. P(A) = 1 – P(A`) = 1 – 0.237 = 0.763

We often describe the union of events using the word or. Rule for Computing the Probability of a Union of Two Events-If E and F are events, then P(E  F) = P(E) + P(F) – P(E  F). If E and F have no outcomes in common, they are called mutually exclusive events. In this case, because E  F = , the preceding formula simplifies to P(E  F) = P(E) + P(F)

If we select a card from a standard 52-card deck, what is the probability that we draw either a heart or a face card? There are 13 hearts, 12 face cards, and 3 cards that are both hearts and face card. P(H  F) = P(H) + P(F) – P(H  F) = 13 + 12 – 3 = 22 = 11 52 52 52 52 26

We may use several formulas to calculate an event’s probability. Out of 1600 people surveyed, 496 have an income above $60,000, 480 spend ten or more hours shopping on the Internet, and 192 have an income above $60,000 and spend ten or more hours shopping on the Internet. What is the probability that a person neither shops on the Internet ten or more hours nor has an income above $60,000?

P(T) = 480 = 0.30 1600 P(I) = 496 = 0.31 1600 P(T I) = 192 = 0.12 1600 P((T  I)`) = 1 – P(T  I) = 1 – (0.30 + 0.31 – 0.12) = 0.51

Classwork/Homework Classwork – Page 743 (5 – 27 odd) Homework – Page 743(6 – 28 even)