SECTION 3.1 Basic Concepts of Probability and Counting 143 Graphical Analysis In Exercises 63 and 64, use the diagram at the left. 63. What is the probability that a voter from West Virginia chosen at random voted Republican in the 2020 governor’s election? (Source: West Virginia State) 64. What is the probability that a registered voter in Texas chosen at random did not vote in the 2020 presidential election? (Source: Texas Secretary of State) 65. Access Code An access code consists of three digits. Each digit can be any number from 0 through 9, and each digit can be repeated. (a) What is the probability of randomly selecting the correct access code on the first try? (b) What is the probability of not selecting the correct access code on the first try? 66. Access Code An access code consists of six characters. For each character, any letter or number can be used, with the exceptions that the first character cannot be 0 and the last two characters must be odd numbers. (a) What is the probability of randomly selecting the correct access code on the first try? (b) What is the probability of not selecting the correct access code on the first try? Using a Tree Diagram In Exercises 67–70, a probability experiment consists of rolling a six-sided die and spinning the spinner shown at the left. The spinner is equally likely to land on each color. Use a tree diagram to find the probability of the event. Then explain whether the event can be considered unusual. 67. Event A: rolling a 5 and the spinner landing on blue 68. Event B: rolling an odd number and the spinner landing on green 69. Event C: rolling a number less than 6 and the spinner landing on yellow 70. Event D: not rolling a number less than 6 and the spinner landing on yellow Boy or Girl? In Exercises 71–74, a couple plans to have three children. Each child is equally likely to be a boy or a girl. 71. What is the probability that all three children are girls? 72. What is the probability that all three children are boys? 73. What is the probability that exactly one child is a girl? 74. What is the probability that at least one child is a boy? Using a Bar Graph to Find Probabilities In Exercises 75– 78, use the bar graph at the left, which shows the highest level of education received by employees of a company. Find the probability that the highest level of education for an employee chosen at random is 75. a doctorate. 76. an associate’s degree. 77. a master’s degree. 78. a high school diploma. 79. Unusual Events Can any of the events in Exercises 49–52 be considered unusual? Explain. 80. Unusual Events Can any of the events in Exercises 75–78 be considered unusual? Explain. 5 10 15 20 25 30 35 Number of employees Doctoral Master’s Bachelor’s Other Highest level of education Associate’s High school diploma Level of Education 25 23 4 3 2 34 FIGURE FOR EXERCISES 75–78 FIGURE FOR EXERCISES 67–70 497,944 voted Republican 270,860 voted for another party 2020 West Virginia Governor’s Election Voters FIGURE FOR EXERCISE 63 11,315,056 voted in the 2020 presidential election 5,640,463 did not vote in the 2020 presidential election All Registered Voters in Texas FIGURE FOR EXERCISE 64
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