← Grade 7: Probability and Statistics
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Grade 7: Probability and Statistics
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Grade 7: Probability and Statistics — Flashcards
| Front | Back |
|---|---|
| What two main topics does this chapter cover? | Probability (including compound events) and Statistics (sampling, inference, and comparing populations). |
| Who is considered a founder of scientific statistics, and why? | Florence Nightingale, a nurse in the Crimean War, who gathered data on hospital sanitation and patient mortality to show that unsanitary conditions—not injuries themselves—caused many soldier deaths. |
| What visual tool did Florence Nightingale invent to persuade Queen Victoria? | The bar graph, used to make her data on hospital mortality visually convincing. |
| What change did Florence Nightingale's data lead Queen Victoria to order? | That physicians should wash their hands, marking the start of scientific statistics and modern medical practice. |
| Who were Blaise Pascal and Pierre Fermat, and why are they important to probability? | Two 17th-century mathematicians who developed the foundations of probability theory after the Chevalier de Méré asked Pascal about a dice game puzzle. |
| What is the Law of Large Numbers? | The idea that an unknown probability can be estimated by repeating a trial many times and calculating the proportion of times a particular outcome occurs. |
| What real classroom experiment illustrates the Law of Large Numbers? | Tossing a Hershey's Kiss many times and calculating the proportion of times it lands on its base. |
| What is inferential statistics? | Using samples collected from a population to make judgments (inferences) about characteristics of the whole population, since populations are usually too large to measure directly. |
| Why must samples be selected randomly? | Random selection helps ensure the sample fairly represents the characteristics of the entire population. |
| What are the four parts of a "simple game" as defined in this chapter? | Players, a tableau (playing field), moves (actions players can take), and outcomes (end positions), plus a rule for determining the winner. |
| What makes a game "fair"? | A game is fair if all outcomes are equally likely, meaning each player has an equal chance of winning. |
| What is the difference between a "simple" game and a "compound" game? | In a simple game, each outcome belongs to exactly one player's winning event; in a compound game (like casino bets), players' chosen winning events can overlap. |
| In the two-spinner game, why was giving Player A all odd digits and Player B all even digits NOT fair? | Because there are 5 odd and 5 even digits, giving 25 total outcomes (an odd number), which cannot be split evenly between two players. |
| In the six-vs-five spinner example (Example 2), how was the game shown to be fair? | With 6×5 = 30 total outcomes, counting showed Player A won in 15 outcomes and lost in 15 outcomes, splitting the outcomes evenly. |
| What are organized lists, tables, and tree diagrams used for in this chapter? | Displaying and analyzing compound events to determine their probabilities. |
| What game illustrates that a game can appear fair but actually isn't? | "Player B Always Wins," using four spinners (Red, Blue, Green, Yellow) where the second player can always choose a spinner that gives them better odds. |
| What is the strategy for Player B to guarantee better odds in the four-spinner game? | Player B should always choose the spinner listed directly after the one Player A picked (e.g., if A picks Yellow, B should pick Red). |
| What is the purpose of the "Teacher Always Wins!" anchor problem? | To introduce students to thinking about what data are needed to determine whether a game is fair, and to show that such analysis is not always simple. |
| What famous problem, explored later in Section 1, also shows that fairness/probability isn't always intuitive? | The Monty Hall problem. |
| What skills do students strengthen while performing probability calculations in this chapter? | Working with fractions and decimals and performing rational number operations. |
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