Exercises 58 there are 3 prime numbers 2 3 and 5

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Exercises 5–8 There are 3 prime numbers (2, 3, and 5). There is a total of 5 numbers. There is 1 tails side. There is a total of 2 sides. 1 5 4 3 2
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Section 10.5 Independent and Dependent Events 431 Events are dependent events if the occurrence of one event does affect the likelihood that the other event(s) will occur. Probability of Dependent Events Words The probability of two dependent events A and B is the probability of A times the probability of B after A occurs. Symbols P ( A and B ) = P ( A ) P ( B after A ) EXAMPLE Finding the Probability of Dependent Events 2 People are randomly chosen to be game show contestants from an audience of 100 people. You are with 5 of your relatives and 6 other friends. What is the probability that one of your relatives is chosen first, and then one of your friends is chosen second? Choosing an audience member changes the number of audience members left. So, the events are dependent. P (relative) = 5 100 = 1 20 P (friend) = 6 99 = 2 33 Use the formula for the probability of dependent events. P ( A and B ) = P ( A ) P ( B after A ) P (relative and friend) = P (relative) P (friend after relative) = 1 20 2 33 Substitute. = 1 330 Simplify. The probability is 1 330 , or about 0.3%. 2. What is the probability that you, your relatives, and your friends are not chosen to be either of the first two contestants? Exercises 9–12 There are 5 relatives. There are 6 friends. There is a total of 100 audience members. There is a total of 99 audience members left.
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432 Chapter 10 Probability and Statistics Exercises 18–22 EXAMPLE Finding the Probability of a Compound Event 3 A student randomly guesses the answer for each of the multiple-choice questions. What is the probability of answering all three questions correctly? Choosing the answer for one question does not affect the choice for the other questions. So, the events are independent. Method 1: Use the formula for the probability of independent events. P (#1 and #2 and #3 correct) = P (#1 correct) P (#2 correct) P (#3 correct) = 1 5 1 5 1 5 Substitute. = 1 125 Multiply. The probability of answering all three questions correctly is 1 125 , or 0.8%. Method 2: Use the Fundamental Counting Principle. There are 5 choices for each question, so there are 5 5 5 = 125 possible outcomes. There is only 1 way to answer all three questions correctly. P (#1 and #2 and #3 correct) = 1 125 The probability of answering all three questions correctly is 1 125 , or 0.8%. 3. The student can eliminate Choice A for all three questions. What is the probability of answering all three questions correctly? Compare this probability with the probability in Example 3. What do you notice? 1. In what year did the United States gain independence from Britain? A. 1492 B. 1776 C. 1788 D. 1795 E. 2000 3. In what year did the Boston Tea Party occur?
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