11.6 Conditional Probability 717 8. a) a 5 or a 7. 2 13 b) a 5 or a 7, given that the card is not a face card. 1 5 Tennis Balls In Exercises 9–14, consider the tennis balls in the figure below. 1 2 3 4 5 6 Assume that one tennis ball is randomly selected. Determine the probability that the ball selected shows 9. a) a 5. 1 6 b) a 5 given that the ball is orange. 1 3 10. a) a 6. 1 6 b) a 6, given that the ball is yellow. 1 2 11. a) an even number. 1 2 b) an even number, given that the ball is orange. 1 3 12. a) an odd number. 1 2 b) an odd number, given that the ball is orange. 2 3 13. a) a red number. 1 3 b) a red number, given that the ball is yellow. 0 14. a) a black number. 2 3 b) a black number, given that the ball is yellow. 1 Select a Number In Exercises 15–20, consider the following figures. 3 4 1 6 2 5 7 Assume that one figure is randomly selected and each figure is equally likely to be selected. Determine the probability of selecting 15. a circle, given that an odd number is selected. 3 4 16. a triangle, given that a number greater than or equal to 5 is selected. 1 3 17. an odd number, given that a circle is selected. 1 18. a number greater than or equal to 5, given that a triangle is selected. 1 2 19. a circle or square, given that a number less than 4 is selected. 2 3 20. a triangle, given that an odd number is selected. 0 Spin the Wheel In Exercises 21–28, consider the following wheel. If the wheel is spun and each section is equally likely to stop under the pointer, determine the probability that the pointer lands on 21. an even number, given that the color is purple. 3 5 22. an odd number, given that the color is red. 2 3 23. purple, given that the number is even. 1 2 24. red, given that the number is odd. 1 3 25. a number greater than 4, given that the color is purple. 3 5 26. an even number, given that the color is red or purple. 1 2 27. gold, given that the number is greater than 5. 1 7 28. gold, given that the number is greater than 10. 0 Money from a Hat In Exercises 29–32, assume that a hat contains four bills: a $1 bill, a $5 bill, a $10 bill, and a $20 bill. Each bill is equally likely to be selected. Two bills are to be randomly selected with replacement. Construct a sample space as was done in Example 2 and determine the probability that 29. both bills are $1 bills. 1 16 30. both bills are $1 bills if the first selected is a $1 bill. 1 4 31. both bills are $5 bills if at least one of the bills is a $5 bill. 1 7 32. both bills have a value greater than a $5 bill if the second bill is a $10 bill. 1 2 Two Dice In Exercises 33–38, two fair dice are rolled one after the other. Construct a sample space and determine the probability that the sum of the dots on the dice total 2 3 7 1 9 4 6 12 10 5 11 8 Viktor Fedorenko/ Shutterstock.
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