C Challenge

44. Suppose you roll a red number cube and a yellow number cube.
    1. What is P(red 1 and yellow 1)?
    2. What is P(red 2 and yellow 2)?
    3. What is the probability of rolling any matching pair of numbers? (Hint: Add the probabilities of each of the six matches.)
45. A two-digit number is formed by randomly selecting from the digits 1, 2, 3, and 5 without replacement.
    1. How many different two-digit numbers can be formed?
    2. What is the probability that a two-digit number contains a 2 or a 5?
    3. What is the probability that a two-digit number is prime?

Standardized Test Prep

SAT/ACT

46. You take a three-question true-or-false quiz. You guess on all the questions. What is the probability that you will get a perfect score?
    1. 1
    2. 1 2 1 half
    3. 1 4 1 fourth
    4. 1 8 1 eighth
47. You have a bag containing 3 green marbles, 4 red marbles, and 2 yellow marbles. You select 1 marble randomly. What are the odds against selecting a green or yellow marble?
    6. 5 : 4
    7. 9 : 4
    8. 4 : 9
    9. 4 : 5

Extended Response

48. A survey at your school is being taken to gather student input on the items offered by the cafeteria.
    1. Possible sampling methods are asking the nutrition club, asking the boys' wrestling team, and asking 5 students from each homeroom. Explain whether or not each sample could lead to biased results.
    2. Write a question designed to encourage respondents to favor more pizza. Then write another question about menu choices that is unbiased.

Mixed Review

See Lesson 12-7.

You select a number at random from the integers 10 through 30, inclusive. Find each probability.

49. P(number is even)
50. P(number is a multiple of 6)
51. P(number is prime)
52. P(number is less than 18)

See Lesson 11-2.

Simplify each complex fraction.

53. − 12 q − 10 6 q + 5 11 fraction negative 12 q minus 10 , over fraction 6 q plus 5 , over 11 end fraction end fraction
54. 3 a + 2 a 2 − 10 a + 25 15 a + 10 a 2 − 25 fraction fraction 3 eh plus 2 , over eh squared , minus 10 eh plus 25 end fraction , over fraction 15 eh plus 10 , over eh squared , minus 25 end fraction end fraction
55. 7 y 2 + 6 y − 1 y + 3 49 y 2 − 1 7 y + 21 fraction fraction 7 , y squared , plus 6 y minus 1 , over y plus 3 end fraction , over fraction 49 , y squared , minus 1 , over 7 y plus 21 end fraction end fraction

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