4-1 Basic Concepts of Probability 151 Complementary Events Sometimes we need to find the probability that an event A does not occur. b. It is certain that a Thanksgiving Day in the United States will be on a Thursday. When an event is certain to occur, its probability is 1. P(Thanksgiving on Thursday) = 1. Because any event imaginable is impossible, certain, or somewhere in between, it follows that the mathematical probability of any event A is 0, 1, or a number between 0 and 1 (as shown in Figure 4-2). For those of us into mathematical notation, we can express this as 0 … P1A2 … 1. YOUR TURN. Do Exercises 19 “Square Peg” and 20 “Death and Taxes.” DEFINITION The complement of event A, denoted by A, consists of all outcomes in which event A does not occur. SOLUTION Among 2002 survey subjects, 1782 use the Internet, so it follows that the other 220 do not use the Internet. We get the following P1not using the Internet2 = 220 2002 = 0.110 INTERPRETATION The probability of randomly selecting an adult who does not use the Internet is 0.110. Complement of Internet User EXAMPLE 8 In a Pew Research Center survey of 2002 randomly selected adults, 1782 of those respondents said that they use the Internet. Find the probability that a randomly selected adult does not use the Internet. YOUR TURN. Do Exercise 25 “Social Networking.” Relationship Between P1A2 and P1A2 If we denote the event of an adult using the Internet by I, we get P1I2 = 1782>2002 = 0.890 and P1I2 = 0.110. P1I2 could be found by just subtracting P1I2 from 1. Go Figure 1080: Number of particles in the observable universe. The probability of a monkey randomly hitting keys and typing Shakespeare’s Hamlet is 10-216,159.
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