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Listing Outcomes Sample Space Diagrams — Free MYP2 Mathematics Practice Questions
1QuestionCounting Outcomes for Combined EventsConcept Practice
2 marks~3 minCriterion A
A coin is flipped twice. The tree diagram shows all possible outcomes.
a
State the number of outcomes for each single flip. [1]
b
Using the tree diagram, identify all distinct outcomes for two flips and state the total number of outcomes. [1]
Solutions
2QuestionCounting Outcomes for Combined EventsAssessment Practice
6 marks~9 minCriterion C
A board game uses two fair six-sided dice. A player must roll a total of 7 to start. The rulebook claims: "All totals from 2 to 12 are equally likely."
a
Draw a sample space diagram showing all 36 possible outcomes. Use it to calculate the probability of rolling a total of 7. [2]
b
Explain why the rulebook's claim is incorrect. Use values from your diagram to support your answer. [2]
c
A second set of dice is slightly weighted so each die is more likely to land on 6. Compare how this would affect the probability of rolling a total of 7, and state whether your diagram from part (a) would still be useful. [2]
Solutions
3QuestionCounting Outcomes for Combined EventsAssessment Practice
8 marks~12 minCriterion D
A school canteen offers 3 main dishes, 2 sides, and 4 drinks. The manager says there are exactly 24 possible meal combinations.
a
State the number of choices for each item and calculate the total number of meal combinations. [2]
b
Explain two real-world factors that could reduce the number of practical meal combinations. [2]
c
Compare the usefulness of the 24-combination count for the manager's planning with its limitations as a real-world model. [4]
Solutions
4QuestionCounting Outcomes for Combined EventsAssessment Practice
2 marks~3 minCriterion B
A 6-sided die is rolled and some coins are flipped. The table below shows the total number of possible outcomes.
| Number of coins | 1 | 2 | 3 |
|---|---|---|---|
| Total outcomes | 12 | 24 | 48 |
a
Identify the pattern in the total outcomes as the number of coins increases. [1]
b
State the total outcomes for 4 coins and write the general rule for finding the total outcomes when rolling one 6-sided die and flipping coins. [1]
Solutions
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