4-1 Basic Concepts of Probability 145 20 Girls Statisticians reject explanations based on very low probabilities Test A Result Probability of 20 Girls by chance 5 954 in 1,000,000,000 5 0.000000954 Chance rejected as reasonable explanation Gender selection method appears to be effective 0 Boys 12 Girls Test B Result Probability of 12 (or more) Girls by chance 5 251,722 in 1,000,000 5 0.251722 Chance not rejected as reasonable explanation Cannot conclude gender selection method is effective 8 Boys Different Gender Selection Methods Tested with 20 Births FIGURE 4-1 Gender Selection Method Test Data and Conclusions Figure 4-1 shows the sample data from two tests of couples using the gender selection method and the conclusion reached for each test. YOUR TURN. Do Exercise 37 “Predicting Gender.” INTERPRETATION Among the 20 babies, 20 girls and 12 girls are both greater than the 10 girls that we typically expect, but only the event of 20 girls leads us to believe that the gender selection method is effective. Even though there is a chance of getting 20 girls in 20 births with no special treatment, the probability of that happening is so small (0.000000954) that we should reject chance as a reasonable explanation. Instead, it would be generally recognized that the results provide strong support for the claim that the gender selection method is effective. This is exactly how statisticians think: They reject explanations (such as chance) based on very low probabilities. Basics of Probability In probability, we deal with procedures (such as generating male>female births or answering a multiple choice test question) that produce outcomes. DEFINITIONS An event is any collection of results or outcomes of a procedure. A simple event is an outcome or an event that cannot be further broken down into simpler components. The sample space for a procedure consists of all possible simple events. That is, the sample space consists of all outcomes that cannot be broken down any further. Example 2 illustrates the concepts defined above.
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