A focused Grade 7 learning session for Theoretical Probability using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving theoretical probability.
Theoretical Probability is part of Grade 7 Probability. This activity focuses on the central idea students need before they move into independent practice.
Students will build Grade 7 mastery of theoretical probability using models, equations, and test-style reasoning.
| What to notice | How to use it |
|---|---|
| Numbers, units, labels, diagrams, or graphs | Identify what each part represents before calculating. |
| The relationship in the problem | Connect the model to an equation, comparison, or explanation. |
Use the figures and worked questions in the practice set below as the visual model for this skill.
Read the first practice question slowly. Decide what the question is asking, choose a strategy, solve, and then compare your reasoning with the answer explanation.
For Theoretical Probability, a strong worked example should show the setup, the calculation or model, and a final answer that matches the context.
Many Grade 7 test questions use real situations. Look for quantities, units, rates, measures, expressions, or data values that connect the math to the story.
After solving, explain what the answer means in the situation, not just the number you calculated.
I can solve problems involving theoretical probability.
Use the warmup, guided question, practice set, and exit questions below to check whether this skill is ready or needs more practice.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
A bag contains \(4\) red, \(5\) blue, and \(6\) green marbles. What is the theoretical probability of drawing a blue marble at random?
Answer B: \(\frac{1}{3}\)
Total \(=4+5+6=15\). \(P(\text{blue})=\frac{5}{15}=\frac{1}{3}\).
A fair six-sided die is rolled once. What is the probability of rolling a number greater than \(4\)?
Answer B: \(\frac{1}{3}\)
Favorable outcomes: \(5, 6\) (two outcomes). Total outcomes: \(6\). \(P(\text{>4})=\frac{2}{6}=\frac{1}{3}\).
A spinner is divided into \(4\) equal sections: Red, Yellow, Blue, and Green. What is the probability of spinning Red or Green?
Answer B: \(\frac{1}{2}\)
Each section is \(\frac{1}{4}\). Red + Green \(= \frac{1}{4} + \frac{1}{4} = \frac{1}{2}\).
A jar holds \(3\) yellow, \(4\) purple, and \(8\) orange tokens. If a token is drawn at random, what is the theoretical probability it is purple?
Answer A: \(\frac{4}{15}\)
Total tokens \(= 3 + 4 + 8 = 15\). \(P(\text{purple})=\frac{4}{15}\).
A restaurant menu has \(12\) desserts: \(5\) chocolate, \(4\) fruit, and \(3\) cream-based. If you pick one at random, what is the probability of choosing a chocolate or cream-based dessert?
Answer C: \(\frac{2}{3}\)
Chocolate or cream-based: \(5 + 3 = 8\). \(P=\frac{8}{12}=\frac{2}{3}\).
A fair coin is flipped. What is the theoretical probability of getting heads?
Answer C: \(\frac{1}{2}\)
A fair coin has two equally likely outcomes: heads and tails. \(P(\text{heads})=\frac{1}{2}\).
A bag contains \(6\) white socks and \(4\) black socks. A sock is drawn at random. What is the probability of drawing a white sock?
Answer A: \(\frac{3}{5}\)
Total socks \(= 6 + 4 = 10\). \(P(\text{white})=\frac{6}{10}=\frac{3}{5}\).
A number cube is labeled with the numbers \(1, 2, 2, 3, 3, 3\). When rolled, what is the probability of rolling a \(3\)?
Answer B: \(\frac{1}{2}\)
Three faces show \(3\). Total faces: \(6\). \(P(\text{rolling } 3)=\frac{3}{6}=\frac{1}{2}\).
A box contains cards numbered \(5\) through \(14\). A card is drawn at random. What is the probability of drawing a card with a number divisible by \(3\)?
Answer B: \(\frac{3}{10}\)
Numbers: \(5, 6, 7, 8, 9, 10, 11, 12, 13, 14\) (10 total). Divisible by \(3\): \(6, 9, 12\) (3 outcomes). \(P=\frac{3}{10}\).
A spinner has four equal sections labeled \(A, B, C, D\), where sections \(A\) and \(B\) are blue and sections \(C\) and \(D\) are red. What is the probability of landing on a red section?
Answer B: \(\frac{1}{2}\)
Red sections: \(C\) and \(D\) (2 out of 4). \(P(\text{red})=\frac{2}{4}=\frac{1}{2}\).
A bag contains \(2\) dimes, \(3\) nickels, and \(5\) pennies. A coin is picked at random. What is the probability of not picking a penny?
Answer B: \(\frac{5}{10}\)
Total coins \(= 2 + 3 + 5 = 10\). Non-penny coins \(= 2 + 3 = 5\). \(P(\text{not penny})=\frac{5}{10}=\frac{1}{2}\).
