Grade 7: Probability and Statistics — Quiz

Multiple Choice

1. Who is credited with beginning the field of scientific statistics through her work during the Crimean War?
A. Queen Victoria
B. Florence Nightingale
C. Blaise Pascal
D. Chevalier de Méré

2. What type of graph did Florence Nightingale invent to convince Queen Victoria of the need for sanitary reform?
A. Line graph
B. Scatter plot
C. Bar graph
D. Tree diagram

3. According to the chapter, Nightingale discovered that many soldiers were dying from:
A. Injuries sustained in battle
B. Complications from unsanitary hospital conditions
C. Lack of food supplies
D. Extreme cold weather

4. Who asked Blaise Pascal about a dice game rule that led to the historical development of probability theory?
A. Pierre Fermat
B. Queen Victoria
C. Chevalier de Méré
D. Florence Nightingale

5. What is the name of the method used to estimate an unknown probability by repeating a trial many times (such as tossing a Hershey's Kiss)?
A. The Fairness Rule
B. The Law of Large Numbers
C. Inferential Statistics
D. The Sampling Theorem

6. In Section 2 of the chapter, what is the key requirement for a sample to accurately represent a population?
A. The sample must be very large
B. The sample must be selected randomly
C. The sample must include the entire population
D. The sample must be chosen by the teacher

7. A "simple game" is described in the chapter as having players, a tableau, moves, outcomes, and:
A. A scoreboard
B. A rule to decide the winner
C. A time limit
D. A set of dice

8. In the Two Spinner Game example, if Player A's spinner has {0,1,2,3,4} and Player B's spinner has {5,6,7,8,9}, the game is:
A. Fair, because each spinner has 5 numbers
B. Not fair, because Player B always wins
C. Not fair, because Player A always wins
D. Fair, because the outcomes are random

Short Answer

9. Explain what it means for a game to be called "fair," according to the chapter's definition.

10. In Example 2, Player A's spinner has {0, 2, 4, 6, 8, 10} and Player B's spinner has {1, 3, 5, 7, 9}. Explain, using the reasoning from the text, why this game is fair.

11. What is the difference between how probability and statistics developed historically, according to the chapter's introduction?

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Answer Key

1. B — Florence Nightingale
2. C — Bar graph
3. B — Complications from unsanitary hospital conditions
4. C — Chevalier de Méré
5. B — The Law of Large Numbers
6. B — The sample must be selected randomly
7. B — A rule to decide the winner
8. B — Not fair, because Player B always wins

1. A game is fair if all the outcomes are equally likely (for example, the set of outcomes where Player A wins and the set where Player B wins have the same number of outcomes).

1. There are 6 × 5 = 30 total possible outcomes. Counting the pairs where A wins (a > b): A loses in 5 + 4 + 3 + 2 + 1 = 15 outcomes, so A also wins in 15 outcomes. Since 15 = 15, both players have an equal number of winning outcomes out of 30, making the game fair.

1. Probability arose from games of chance (e.g., gamblers' questions like the Chevalier de Méré's dice problem, leading Pascal and Fermat to develop probability theory), while statistics arose from the need to analyze real-world data to solve practical problems (e.g., Florence Nightingale's analysis of hospital mortality data during the Crimean War).