Using Tree Diagrams and Venn Diagrams Introductory

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Using Tree Diagrams and Venn Diagrams Introductory — Free MYP2 Mathematics Practice Questions

1QuestionCalculating Basic Probabilities Using Tree DiagramsConcept Practice

2 marks~3 minCriterion A

A spinner has two sections,

A

and

B

. The probability of landing on

A

0.6

and the probability of landing on

B

0.4

for each spin. The spinner is spun twice.

Identify the probability of landing on

A

on the first spin and

B

on the second spin. [1]

Calculate

P(A \text{ then } B)

. [1]

Solutions

2QuestionExploring Overlapping and Disjoint EventsAssessment Practice

2 marks~3 minCriterion D

A school cafeteria manager records that 60 students buy pizza, 30 buy salad, and 15 buy both.

Describe one way this data helps the manager decide how much food to prepare. [1]

Identify one limitation of using a Venn diagram to plan food orders, and explain why it creates a problem. [1]

Solutions

3QuestionUnderstanding Tree Diagrams for Two EventsAssessment Practice

5 marks~8 minCriterion C

A fair spinner has three equal sections labelled A, B, and C. It is spun twice. A student's tree diagram shows the probability of A on the first spin as

\frac{1}{2}

and on the second spin as

\frac{1}{3}

, giving

P(\text{A and A}) = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}

Identify the error in the tree diagram. [1]

Calculate the correct probability of getting A on both spins. Show your working using the multiplication rule for independent events (where the result of one spin does not affect the other). [2]

A classmate says: "It doesn't matter which spin has the wrong probability — the final answer

\frac{1}{6}

is close enough to

\frac{1}{9}

, so the error is not important." Compare the two probabilities and explain why the error does matter. [2]

Solutions

4QuestionInterpreting Simple Venn DiagramsAssessment Practice

6 marks~9 minCriterion B

A Venn diagram shows two sets,

A

and

B

, inside a universal set

\xi

of 20 elements, where

n(A) = 10

and

n(B) = 8

The intersection

A \cap B

(the overlap of

A

and

B

) contains 6 elements. Calculate

n(A \cup B)

, the total number of elements in

A

B

. [2]

The table below shows four diagrams with different intersection sizes.

n(A \cap B)

: 2, 4, 6, 8

n(A \cup B)^{\prime}

(complement): ?, ?, ?, ?

Calculate the complement size for each intersection value. Describe the pattern you notice. [3]

A fifth diagram has

n(A \cap B) = 5

. Using your pattern, estimate the complement size and explain why your answer is reasonable. [1]

Solutions

Questions 5-60

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