154 CHAPTER 4 Probability Statistical Literacy and Critical Thinking 1.California Lottery Let A denote the event of placing a $1 straight bet on the California Daily 4 lottery and winning. There are 10,000 different ways that you can select the four digits (with repetition allowed) in this lottery, and only one of those four-digit numbers will be the winner. What is the value of P1A2? What is the value of P1A2? 2. Probability Rewrite the following statement so that the likelihood of rain is expressed as a value between 0 and 1: “The probability of rain today is 25%.” 3.Dice and Coins a. Find the probability that when a single six-sided die is rolled, the outcome is 5. b. Find the probability that when a coin is tossed, the result is heads. c. Find the probability that when a six-sided die is rolled, the outcome is 7. 4.Subjective Probability Estimate the probability that the next time that you approach an escalator, you find it to be in operation. 5.Identifying Probability Values Which of the following are probabilities? 0 3>5 5>3 -0.25 250, 7:3 1 50950 5:1 0.135 2.017 6. Penicillin “Who discovered penicillin: Marcel Bich, William Penn, Jonas Salk, Alexander Fleming, or Louis Pasteur?” If you make a random guess for the answer to that question, what is the probability that your answer is the correct answer of Alexander Fleming? 7.Planck’s Constant If you are asked on a quiz to give the first digit of the Planck constant and, not knowing the answer, you make a random guess, what is the probability that your answer is the correct answer of 6? 8.Sample Space for Births Example 2 in this section includes the sample space for genders from three births. Identify the sample space for the genders from two births. In Exercises 9–12, assume that 100 births are randomly selected. Use subjective judgment to describe the given number of girls as (a) significantly low, (b) significantly high, or (c) neither significantly low nor significantly high. 9. 53 girls. 10. 35 girls. 11. 75 girls. 12. 48 girls. In Exercises 13–20, express the indicated degree of likelihood as a probability value between 0 and 1. 13. Testing If you make a random guess for the answer to a true>false test question, there is a 50–50 chance of being correct. 14.SAT Test When making a random guess for an answer to a multiple choice question on an SAT test, the possible answers are a, b, c, d, e, so there is 1 chance in 5 of being correct. 15.Movies Based on a study of the movies made in a recent year, 33 out of every 100 movies have a female lead or co-lead. 16.Online Shopping Based on a National Retail Federation survey, 47% of consumers turn down an online purchase if shipping is not free. 17. Randomness When using a computer to randomly generate the last digit of a phone number to be called for a survey, there is 1 chance in 10 that the last digit is zero. 18. Job Applicant Mistakes Based on an Adecco survey of hiring managers who were asked to identify the biggest mistakes that job candidates make during an interview, there is a 50–50 chance that they will identify “inappropriate attire.” 4-1 Basic Skills and Concepts
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