4-1 Basic Skills and Concepts Statistical Literacy and Critical Thinking 1. New Jersey Lottery Let A denote the event of placing a $1 straight bet on the New Jersey Pick 3 lottery and winning. There are 1000 different ways that you can select the three digits (with repetition allowed) in this lottery, and only one of those three-digit numbers will be the winner. What is the value of P(A )? What is the value of P(A)? 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. Interpreting Weather While this exercise was being created, Weather.com indicated that there was a 60% chance of rain for the author's home region. Based on that report, which of the following is the most reasonable interpretation? a. 60% of the author's region will get rain today. b. In the author's region, it will rain for 60% of the day. c. There is a 0.60 probability that it will rain somewhere in the author's region at some point during the day. 4. Subjective Probability Estimate the probability that the next time you turn on a light switch, you discover that a bulb does work. 5. Identifying Probability Values Which of the following are probabilities? 0 3/5 5/3 -0.25 250% 7:3 1 50-50 5:1 0.135 2.017 6. Penicillin "Who discovered penicillin: Sean Penn, William Penn, Penn Jillette, 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. Avogadro Constant If you are asked on a quiz to give the first (leftmost) nonzero digit of the Avogadro 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. 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 50 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. 47 girls. 10. 26 girls. 11. 23 girls. 12. 5 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. Luggage Based on a Harris poll, if you randomly select a traveler, there is a 43% chance that his or her luggage is black. 16. Sleepwalking Based on a report in Neurology magazine, 29.2% of survey respondents have sleepwalked. 17. Randomness When using a computer to randomly generate the last digit of a phone num- her to be called for a survey, there is 1 chance in 10 that the last digit is zero
