Quiz: Probability, Percent & Rational Number Equivalence

Multiple Choice

1. According to the resource, why does the chapter begin with probability instead of a traditional review of arithmetic?
A) Probability is easier than fractions
B) It embeds review of arithmetic in a new, more engaging topic
C) The state requires probability to be taught first
D) Fractions are not needed for probability

2. In this chapter, probabilities are represented as ratios in what form?
A) Part:part only
B) Part:whole
C) Whole:whole
D) Odds only

3. What is the term for the set of all possible outcomes of an experiment?
A) Probability model
B) Sample space
C) Rational number set
D) Batting average

4. Which two concepts of probability do students focus on regarding events?
A) Odds and ratios
B) Fractions and decimals
C) Experimental (empirical) and theoretical
D) Percent and interest

5. A percent is described in the resource as a fraction with what denominator?
A) 10
B) 1
C) 100
D) 1000

6. Who were the two mathematicians that solved Chevalier de Méré's dice problem, marking the beginning of the mathematical theory of probability?
A) Newton and Leibniz
B) Pascal and Fermat
C) Pascal and de Méré
D) Euclid and Pythagoras

7. What was Chevalier de Méré's error in reasoning about the four-roll dice game?
A) He multiplied probabilities instead of adding them
B) He thought probabilities of repeated trials should add rather than multiply
C) He used the wrong number of dice
D) He confused theoretical and experimental probability

Short Answer

8. Explain the two key objectives of Section 2 of this chapter regarding fractions, decimals, and percents.

9. Using the example from the text, if 3/5 of a class are girls, explain how this part:whole relationship can be converted to a part:part ratio, and state that ratio.

10. According to the resource, what is the correct probability of rolling at least one six in four rolls of a die, and how does this compare to Chevalier de Méré's incorrect calculation?

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Answer Key

1. B
2. B
3. B
4. C
5. C
6. B
7. B
8. Students should confidently articulate relationships among equivalent fractions, decimals, and percents using words, models, and symbols, and students should understand and use models to find portions of different wholes.
9. Since 3/5 of the class are girls, 2/5 must be boys; converting to a part:part ratio gives girls:boys = 3:2.
10. The correct probability is 1 − (5/6)⁴, or 51.8%. De Méré incorrectly calculated it as 4 × 1/6 = 2/3 (about 66.7%), because he mistakenly added probabilities instead of using the correct method.