Basic Concepts of Probability and Counting 3.1 130 CHAPTER 3 Probability What You Should Learn How to identify the sample space of a probability experiment and how to identify simple events How to use the Fundamental Counting Principle to find the number of ways two or more events can occur How to distinguish among classical probability, empirical probability, and subjective probability How to find the probability of the complement of an event How to use a tree diagram and the Fundamental Counting Principle to find probabilities Probability Experiments The Fundamental Counting Principle Types of Probability Complementary Events Probability Applications Probability Experiments When weather forecasters say that there is a 90% chance of rain or a physician says there is a 35% chance for a successful surgery, they are stating the likelihood, or probability, that a specific event will occur. Decisions such as “should you go golfing” or “should you proceed with surgery” are often based on these probabilities. In the preceding chapter, you learned about the role of the descriptive branch of statistics. The second branch, inferential statistics, has probability as its foundation, so it is necessary to learn about probability before proceeding. A probability experiment is an action, or trial, through which specific results (counts, measurements, or responses) are obtained. The result of a single trial in a probability experiment is an outcome. The set of all possible outcomes of a probability experiment is the sample space. An event is a subset of the sample space. It may consist of one or more outcomes. DEFINITION Identifying the Sample Space of a Probability Experiment A survey consists of asking people for their blood types (O, A, B, and AB), including whether they are Rh-positive or Rh-negative. Determine the number of outcomes and identify the sample space. SOLUTION There are four blood types: O, A, B, and AB. For each person, they are either Rh-positive or Rh-negative. A tree diagram gives a visual display of the outcomes of a probability experiment by using branches that originate from a starting point. It can be used to find the number of possible outcomes in a sample space as well as individual outcomes. A− A+ Tree Diagram for Blood Types + − O− O+ + − AB− AB+ + − B− B+ + − O T A B AB From the tree diagram, you can see that the sample space has eight possible outcomes, which are listed below. 5O+, O-, A+, A-, B+, B-, AB+, AB-6 Sample space EXAMPLE 1 Study Tip Here is a simple example of the use of the terms probability experiment, sample space, event, and outcome. Probability Experiment: Roll a six-sided die. Sample Space: 51,2,3,4,5,66 Event: Roll an even number, 52, 4, 66. Outcome: Roll a 2, 526.
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