150 CHAPTER 4 Probability Ghosts! EXAMPLE 6 In a Pew Research Center survey, randomly selected adults were asked if they have seen or have been in the presence of a ghost. 366 of the respondents answered “yes,” and 1637 of the respondents answered “no”. Based on these results, find the probability that a randomly selected adult says that they have seen or been in the presence of a ghost. YOUR TURN. Do Exercise 23 “Mendelian Genetics.” CAUTION A common mistake is to blindly plug in numbers to get the wrong probability of 366>1637 = 0.224. We should think carefully about what we are doing, as follows. SOLUTION INTERPRETATION There is a 0.183 probability that a randomly selected adult says that they have seen or been in the presence of a ghost. Instead of trying to determine an answer directly from the given statement, first summarize the information in a format that allows clear understanding, such as this format: 366 responses of “yes” 1637 responses of “no” 2003 total number of responses We can now use the relative frequency approach as follows: P1response of ;yes<2 = number of ;yes< responses total number of responses = 366 2003 = 0.183 CAUTION Don’t make the common mistake of finding a probability value by mindlessly dividing a smaller number by a larger number. Instead, think carefully about the numbers involved and what they represent. Carefully identify the total number of items being considered, as illustrated in Example 6. SOLUTION a. In the United States, Thanksgiving Day always falls on the fourth Thursday in November. It is therefore impossible for Thanksgiving to be on a Wednesday. When an event is impossible, its probability is 0. P(Thanksgiving on Wednesday) = 0. Thanksgiving Day EXAMPLE 7 If a year is selected at random, find the probability that Thanksgiving Day in the United States will be (a) on a Wednesday or (b) on a Thursday.
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