A focused Grade 7 learning session for Finding Probabilities of Compound Events using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving finding probabilities of compound events.
Finding Probabilities of Compound Events 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 finding probabilities of compound events 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 Finding Probabilities of Compound Events, 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 finding probabilities of compound events.
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 fair coin is flipped twice. What is the probability of getting heads BOTH times?
Answer B: \(\frac{1}{4}\)
\(P(H)\cdot P(H)=\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{4}\).
A fair six-sided die is rolled twice. What is the probability of rolling a 3 on the first roll AND a 5 on the second roll?
Answer C: \(\frac{1}{36}\)
\(P(3)\cdot P(5)=\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{36}\) for independent events.
A bag contains 6 white marbles and 4 black marbles. One marble is drawn at random. What is the probability it is white?
Answer B: \(\frac{3}{5}\)
Total marbles: 10. White marbles: 6. Probability: \(\frac{6}{10}=\frac{3}{5}\).
Two cards are drawn from a standard 52-card deck WITH replacement. What is the probability of drawing a heart on the first draw AND a spade on the second draw?
Answer A: \(\frac{1}{16}\)
With replacement: \(P(\text{heart})\cdot P(\text{spade})=\frac{1}{4}\cdot\frac{1}{4}=\frac{1}{16}\).
A bag contains 3 red marbles and 5 blue marbles. What is the probability of drawing a red marble first, WITHOUT replacing it, then drawing a blue marble?
Answer C: \(\frac{15}{56}\)
Without replacement: \(P(\text{red first})=\frac{3}{8}\), then \(P(\text{blue second})=\frac{5}{7}\) (only 7 left). Product: \(\frac{3}{8}\cdot\frac{5}{7}=\frac{15}{56}\).
Which of the following describes mutually exclusive events?
Answer D: Flipping heads AND flipping tails on one coin flip
Mutually exclusive events cannot happen at the same time. A coin cannot show both heads and tails on one flip.
A card is drawn from a standard deck. What is the probability of drawing a king OR a queen?
Answer B: \(\frac{2}{13}\)
King OR Queen: \(P(\text{King})+P(\text{Queen})=\frac{4}{52}+\frac{4}{52}=\frac{8}{52}=\frac{2}{13}\) (mutually exclusive).
A bag has 10 marbles: 4 red, 3 blue, and 3 green. If you draw one marble, what is the probability of drawing red OR blue?
Answer A: \(\frac{7}{10}\)
Mutually exclusive: \(P(\text{red})+P(\text{blue})=\frac{4}{10}+\frac{3}{10}=\frac{7}{10}\).
A number from 1 to 20 is selected at random. What is the probability of selecting a multiple of 3 OR a multiple of 5?
Answer B: \(\frac{9}{20}\)
Multiples of 3: {3, 6, 9, 12, 15, 18} and multiples of 5: {5, 10, 15, 20}. Total: {3, 5, 6, 9, 10, 12, 15, 18, 20} = 9 numbers. So \(\frac{9}{20}\).
A spinner is divided into 8 equal sections numbered 1 through 8. What is the probability of spinning an odd number OR a prime number?
Answer C: \(\frac{7}{8}\)
Odd: {1, 3, 5, 7}; Prime: {2, 3, 5, 7}. Union: {1, 2, 3, 5, 7} = 7 out of 8.
Consider the sample space for flipping a coin and rolling a die. How many total possible outcomes are there?
Answer C: 12
Coin outcomes: 2 (H, T); Die outcomes: 6. Total: \(2\times 6=12\).
