SECTION 3.1 Basic Concepts of Probability and Counting 131 TRY IT YOURSELF 1 For each probability experiment, determine the number of outcomes and identify the sample space. 1. A probability experiment consists of recording a response to the survey question at the left and the gender of the respondent. 2. A probability experiment consists of recording a response to the survey question at the left and the age (18–34, 35–49, 50 and older) of the respondent. 3. A probability experiment consists of recording a response to the survey question at the left and the geographic location (Northeast, South, Midwest, West) of the respondent. Answer: Page A37 In this chapter, you will learn how to calculate the probability or likelihood of an event. Events are often represented by uppercase letters, such as A, B, and C. An event that consists of a single outcome is called a simple event. For instance, consider a probability experiment that consists of tossing a coin and then rolling a six-sided die, as shown in the tree diagram at the left. The event “tossing heads and rolling a 3” is a simple event and can be represented as A = 5H36. Event A has one outcome, so it is a simple event. In contrast, the event “tossing heads and rolling an even number” is not simple because it consists of three possible outcomes and can be represented as B = 5H2, H4, H66. Event B has more than one outcome, so it is not simple. Identifying Simple Events Determine the number of outcomes in each event. Then decide whether each event is simple or not. Explain your reasoning. 1. For quality assurance, you randomly select a machine part from a batch that has been manufactured that day. Event A is selecting a specific defective machine part. 2. You roll a six-sided die. Event B is rolling at least a 4. SOLUTION 1. Event A has only one outcome: choosing the specific defective machine part. So, the event is a simple event. 2. Event B has three outcomes: rolling a 4, a 5, or a 6. Because the event has more than one outcome, it is not simple. TRY IT YOURSELF 2 You ask for a student’s age at their last birthday. Determine the number of outcomes in each event. Then decide whether each event is simple or not. Explain your reasoning. 1. Event C: The student’s age is between 18 and 23, inclusive. 2. Event D: The student’s age is 20. Answer: Page A37 EXAMPLE 2 SURVEY Does your favorite team’s win or loss affect your mood? Check one response: Yes No Not sure H T2 T1 T3 T4 T5 T6 T Diagram for Coin and Die Experiment 6 5 4 3 2 1 H2 H1 H3 H4 H5 6 H6 5 4 3 2 1
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