708 CHAPTER 11 Probability Practice the Skills Number Drawing In Exercises 9–12, each of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are written on a separate piece of paper and placed in a hat. One piece of paper is randomly selected from the hat. Use the Venn diagram shown to help you determine the probability that the number selected is 9. odd or greater than 5. 4 5 Odd and greater than 5 U A 9 7 2, 4 Numbers > 5 Odd numbers B 6, 8, 10 1, 3, 5 10. even or less than or equal to 4. 7 10 Even and less than or equal to 4 U A 2 4 5, 7, 9 Numbers ≤ 4 Even numbers B 1, 3 6, 8, 10 11. less than or equal to 3 or greater than 7. 3 5 U A B 4, 5, 6, 7 Numbers > 7 Numbers ≤ 3 Numbers ≤ 3 and > 7 8, 9, 10 1, 2, 3 12. even or odd 1 Even and Odd U A B 2, 4, 6, 8, 10 Even numbers Odd numbers 1, 3, 5, 7, 9 In Exercises 13–18, determine the indicated probability. 13. If P A P B () 0.3, () 0.5, = = and P A( and B) 0.2, = determine P A( or B). 0.6 14. If P A P B () 0.7, () 0.8, = = and P A( and B) 0.6, = determine P A( or B). 0.9 15. If = = P A B P A ( or ) 0.9, ( ) 0.8, and = P B( ) 0.2, determine P A B ( and ). 0.1 16. If P A B P A ( or ) 0.65, () 0.35, = = and P B( ) 0.45, = determine P A( and B). 0.15 17. If = = P A B P A ( or ) 0.7, ( ) 0.6, and = P A B ( and ) 0.3, determine P B ( ). 0.4 18. If = = P A B P B ( or ) 0.6, ( ) 0.3, and = P A B ( and ) 0.1, determine P A( ). 0.4 Roll a Die In Exercises 19–22, a single die is rolled one time. Determine the probability of rolling 19. a 5 or 6. 1 3 20. a number greater than 4 or less than 2. 1 2 21. an odd number or a number greater than 4. 2 3 22. an even number or a number greater than 1. 5 6 Drawing a Card In Exercises 23–28, one card is drawn from a standard 52-card deck. Determine whether the following pairs of events are mutually exclusive and then determine P(A or B). 23. A B drawing a 2, drawing a 3. = = Mutually exclusive; 2 13 24. A B drawing a face card, drawing an ace. = = Mutually exclusive; 4 13 25. A B drawing a 4, drawing a diamond. = = Not Mutually exclusive; 4 13 26. A B drawing a 5, drawing a red card. = = Not Mutually exclusive; 7 13 27. A B drawing a face card, drawing a black card. = = Not Mutually exclusive; 8 13 28. A B drawing a face card, drawing a heart. = = Not Mutually exclusive; 11 26
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