11.1 Empirical and Theoretical Probabilities 659 Example 1 Selecting a Beverage At a Little League concession stand, the last 40 beverage purchases were as follows: 16 bottles of water, 14 bottles of sports drink, and 10 bottles of soda. Using this information, determine the empirical probability that the next beverage purchased is a bottle of a) water. b) sports drink. c) soda. Solution a) Let E be the event that a bottle of water is purchased. Then = = = P E E ( ) number of times has occurred total number of times the experiment has been performed 16 40 2 5 b) Let E be the event that a bottle of sports drink is purchased. Then = = P E( ) 14 40 7 20 c) Let E be the event that a bottle of soda is purchased. Then = = P E( ) 10 40 1 4 ■ Now try Exercise 11 In Example 1, we wrote our answers as fractions in lowest terms. In our next example, we will write our answers using decimal numbers. Throughout this chapter, we will be working with both fractions and decimal numbers. Section 5.3 provides a review of fractions and decimal numbers. Example 2 Blood Pressure Reduction A pharmaceutical company is testing a drug that is supposed to help reduce high blood pressure. The drug is given to 500 individuals with the following outcomes. Blood pressure reduced Blood pressure unchanged Blood pressure increased 379 62 59 If this drug is given to an individual, determine the empirical probability that the person’s blood pressure is (a) reduced, (b) unchanged, (c) increased. Write your answer as a decimal number. Solution a) Let E be the event that the blood pressure is reduced. = = P E( ) 379 500 0.758 b) Let E be the event that the blood pressure is unchanged. = = P E( ) 62 500 0.124 c) Let E be the event that the blood pressure is increased. = = P E( ) 59 500 0.118 ■ Now try Exercise 19
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