← Grade 7: Probability, Percent & Rational Numbers
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Grade 7: Probability, Percent & Rational Numbers
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Grade 7: Probability, Percent & Rational Numbers
| Front | Back |
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| Probability | A branch of mathematics that provides the foundation for statistical analysis of data by assigning numerical values to the likelihood of specific outcomes. |
| Statistics | The set of tools for the analysis of data; used to make qualitative statements about a population based on data. |
| Chance process | An experiment or situation for which the possible outcomes are known but which specific outcome will occur at any run is unknown. |
| Sample space | The set of all possible outcomes for an experiment. |
| Event | A subset of the sample space; its probability can be described as impossible, unlikely, equally likely, likely, or certain, or as a number between 0 and 1 inclusive. |
| Experimental (empirical) probability | Probability determined from the actual results or outcomes of conducting an experiment. |
| Theoretical probability | Probability determined by reasoning mathematically about the possible outcomes, rather than from experimental results. |
| Part:whole relationship | A ratio relationship (used in probability) comparing part of a group to the total group, expressed as fractions, decimals, or percents. |
| Part:part relationship | A ratio comparing one part of a group to another part (rather than to the whole); studied later as "odds" in Chapter 7. |
| Percent | A fraction with a denominator of 100; "per hundred." |
| Rational number equivalence | The understanding that fractions, decimals, and percents are equivalent forms of numbers, all relative to an agreed-upon whole or unit. |
| Blaise Pascal | French mathematician who, with Pierre Fermat, solved Chevalier de Méré's dice probability problem, marking the beginning of the mathematical theory of probability. |
| Chevalier de Méré | A professional gambler whose dice betting problems (involving rolling a six and double sixes) led to the founding of probability theory. |
| Pierre Fermat | Mathematician who worked with Pascal to solve de Méré's dice problem, helping establish the theory of probability. |
| De Méré's first dice game | Betting on rolling a six at least once in four rolls; correct probability is 1 − (5/6)⁴ ≈ 51.8%, not the incorrect sum 4 × 1/6. |
| De Méré's second dice game | Betting on rolling double sixes at least once in 24 rolls of a pair of dice; his incorrect reasoning (24/36) led to losses since probabilities don't simply add. |
| Why probabilities don't add | Repeating an experiment does not mean probabilities of a favorable outcome add together (e.g., 1/6 + 1/6 + 1/6 ≠ probability for 3 rolls); instead, related probabilities multiply. |
| Batting average | A statistic (hits ÷ at-bats) derived from past data but used theoretically to predict the probability of a player getting a hit. |
| Percent problems (discounts, interest, taxes, tips) | Real-world contexts used to practice solving percent and fraction problems, transitioning from models to numeric expressions. |
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