3.3 EXERCISES 162 CHAPTER 3 Probability For Extra Help: MyLab Statistics Building Basic Skills and Vocabulary 1. When two events are mutually exclusive, why is P1A andB2 = 0? 2. Give an example of (a) two events that are mutually exclusive and (b) two events that are not mutually exclusive. True or False? In Exercises 3–6, determine whether the statement is true or false. If it is false, explain why. 3. When two events are mutually exclusive, they have no outcomes in common. 4. When two events are independent, they are also mutually exclusive. 5. The probability that event A or event B will occur is P1Aor B2 = P1A2 + P1B2 + P1A andB2. 6. If events A and B are mutually exclusive, then P1A or B2 = P1A2 + P1B2. Graphical Analysis In Exercises 7 and 8, determine whether the events shown in the Venn diagram are mutually exclusive. Explain your reasoning. 7. Wearing a polo shirt Sample Space: Clothes Wearing Bermuda shorts 8. Sample Space: Grades A student has a GPA of 0.0 for the semester A student has “A”s for the semester in 4 out of 5 classes Using and Interpreting Concepts Recognizing Mutually Exclusive Events In Exercises 9–12, determine whether the events are mutually exclusive. Explain your reasoning. 9. Event A: Randomly select a freshman music major. Event B: Randomly select a music major who is 20 years old. 10. Event A: Randomly select a student with a birthday in April. Event B: Randomly select a student with a birthday in May. 11. Event A: Randomly select a voter who is a registered Republican. Event B: Randomly select a voter who is a registered Democrat. 12. Event A: Randomly select a member of the U.S. Congress. Event B: Randomly select a male U.S. Senator. 13. Students A physics class has 40 students. Of these, 12 students are physics majors and 16 students are minoring in math. Of the physics majors, three are minoring in math. Find the probability that a randomly selected student is minoring in math or a physics major. 14. Conference A teaching conference has an attendance of 6855 people. Of these, 3120 are college professors and 3595 are male. Of the college professors, 1505 are male. Find the probability that a randomly selected attendee is male or a college professor.
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