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Using Tree Diagrams and Venn Diagrams Introductory — Free MYP3 Mathematics Practice Questions
1QuestionCalculating Basic Probabilities Using Tree DiagramsConcept Practice
2 marks~3 minCriterion A
A fair coin is flipped twice. Each flip has two possible outcomes: Heads (H) with probability and Tails (T) with probability .
Calculate the probability of obtaining two Heads (HH), using the branches of the tree diagram shown. [2]
Calculate the probability of obtaining two Heads (HH), using the branches of the tree diagram shown. [2]
Solutions
2QuestionUsing Venn Diagrams to Solve Set ProblemsAssessment Practice
4 marks~6 minCriterion C
A survey of 100 students asked whether they like football (F), basketball (B), both, or neither. The results show: 50 students like football, 40 like basketball, and 15 like both sports.
a
Calculate the number of students who like neither sport. [2]
b
Explain one reason why a Venn diagram may misrepresent survey data that contains errors or inconsistencies. [2]
Solutions
3QuestionCalculating Basic Probabilities Using Tree DiagramsConcept Practice
2 marks~3 minCriterion B
A tree diagram for two independent coin flips gives 4 possible outcomes: HH, HT, TH, TT. A tree diagram for three independent coin flips gives 8 possible outcomes.
a
Describe the pattern in the total number of possible outcomes as the number of flips increases. [1]
b
Calculate the total number of possible outcomes for four independent coin flips. [1]
Solutions
4QuestionCalculating Basic Probabilities Using Tree DiagramsAssessment Practice
6 marks~9 minCriterion D
A game show spinner has 4 equal sections labelled 1, 2, 3, and 4. A contestant wins a prize only if the spinner lands on section 3. The spinner is spun twice, and the two spins are independent.
a
Construct a tree diagram showing all possible outcomes for two spins, labelling each branch with its probability. [2]
b
Calculate the probability that the contestant wins a prize on both spins. Show your working. [2]
c
A manufacturing defect makes the pointer slightly heavier on one side, so section 3 is now less likely to be landed on. Analyse how this defect affects the validity of your probability model, and suggest one way to make the model more reliable. [2]
Solutions
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