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Probability and Outcomes

Probability and Outcomes — Free MYP3 Mathematics Practice Questions

1QuestionConducting Simple Probability ExperimentsConcept Practice

3 marks~5 minCriterion B

A fair coin is flipped 50 times. The results are: Heads: 28 flips, Tails: 22 flips.

Calculate the experimental probability of obtaining heads. [1]

Explain one reason why the experimental probability may differ from the theoretical probability of

0.5

. [1]

A second experiment repeats the same coin flip 500 times. Explain what you would expect to happen to the experimental probability of heads, and why. [1]

Solutions

2QuestionDefining Theoretical ProbabilityConcept Practice

2 marks~3 minCriterion A

A spinner is divided into 4 equal sectors: blue, red, green, and yellow.

Calculate the theoretical probability of landing on blue. Express your answer as a fraction in its simplest form. [1]

Explain why this probability is described as theoretical rather than experimental. [1]

Solutions

3QuestionCalculating Combined Probabilities BasicConcept Practice

2 marks~3 minCriterion A

A class of 8 students was surveyed about the sports they play. The Venn diagram shows Set

F

(football) and Set

B

(basketball): 3 students play only football, 2 play only basketball, 1 plays both, and 2 play neither.

Calculate the probability that a randomly selected student plays both football and basketball. Express your answer as a fraction in its simplest form. [1]

A student is chosen at random. Given that the student plays at least one sport, calculate the probability that they play football. Express your answer as a fraction in its simplest form. [1]

Solutions

4QuestionProbability of Flipping a CoinConcept Practice

2 marks~3 minCriterion B

When flipping a fair coin, the number of possible outcomes grows with each flip.

Number of flips ( $n$ )	1	2	3	4
Number of outcomes	2	4	8	16

Describe the pattern in the number of outcomes as

n

increases. [1]

State the general rule for the number of outcomes for

n

flips, and apply it to predict the number of outcomes for 5 flips. [1]

Solutions

5QuestionCreating Fair and Biased ModelsConcept Practice

2 marks~3 minCriterion A

A spinner is divided into four sectors:

Sector A:

90°

Sector B:

120°

Sector C:

60°

Sector D:

90°

The spinner is spun once.

Calculate the probability of landing on Sector B. [1]

Sector B has the highest probability of being landed on. Explain why the spinner is biased. [1]

Solutions

6QuestionCalculating 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.

Describe the pattern in the total number of possible outcomes as the number of flips increases. [1]

Calculate the total number of possible outcomes for four independent coin flips. [1]

Solutions

7QuestionCalculating 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

\frac{1}{2}

and Tails (T) with probability

\frac{1}{2}

.

Calculate the probability of obtaining two Heads (HH), using the branches of the tree diagram shown. [2]

Solutions

8QuestionProbability Scale from 0 to 1Concept Practice

2 marks~3 minCriterion B

A spinner has equally likely outcomes. The table below shows the probability of landing on one specific colour.

Number of outcomes	2	3	4	5
Probability	$\dfrac{1}{2}$	$\dfrac{1}{3}$	$\dfrac{1}{4}$	$\dfrac{1}{5}$

Calculate the probability of landing on one specific colour for a spinner with 6 equally likely outcomes. [1]

Explain the general rule that connects the number of equally likely outcomes to the probability of landing on any one specific colour. [1]

Solutions

9QuestionDescribing Events as Likely or UnlikelyConcept Practice

2 marks~3 minCriterion A

A spinner is divided into 8 equal sections: 5 red, 2 blue, and 1 green.

Calculate the probability of landing on red. [1]

Explain whether landing on red is likely or unlikely. [1]

Solutions

10QuestionCounting Outcomes for Combined EventsConcept Practice

5 marks~8 minCriterion B

A student investigates outcomes for two independent events.

Event X has 2, 3, or 4 choices. Event Y has 3, 4, or 5 choices. The combined outcomes for each matching pair are 6, 12, and 20 respectively.

Calculate the total outcomes for each pair as a product of the two numbers of choices. [1]

Explain how the pattern from part (a) leads to a general formula for the total number of outcomes when Event X has

m

choices and Event Y has

n

choices. [2]

A spinner has 4 equal sections and a die has 6 faces. Apply your formula to find the total number of outcomes when both are spun or rolled together. Justify whether this total is greater than, equal to, or less than 30. [2]

Solutions

11QuestionCounting Outcomes for Combined EventsConcept Practice

2 marks~3 minCriterion A

A spinner has three equal sections labelled red, blue, and green. A fair coin is tossed at the same time as the spinner is spun.

List all possible combined outcomes of this experiment. Write each outcome as an ordered pair in the format

(\text{spinner colour},\ \text{coin outcome})

. [2]

Solutions

12QuestionComparing Theoretical and Experimental ResultsAssessment Practice

6 marks~9 minCriterion D

A student rolls a fair six-sided die 600 times and records 80 sixes.

Calculate the expected number of sixes in 600 rolls. [2]

Explain why rolling 80 sixes does not necessarily mean the die is biased. In your answer, refer to natural variation and sample size. [2]

The student concludes the die is biased after this single trial. Analyse whether this conclusion is valid, and justify your reasoning. [2]

Solutions

13QuestionUnderstanding Variability in ResultsAssessment Practice

3 marks~5 minCriterion C

A fair coin is flipped 50 times. The results are shown in the bar chart: 28 heads and 22 tails.

Calculate the experimental probability of getting heads. [1]

Explain why the experimental probability differs from the theoretical probability of

0.5

. [1]

A student claims that flipping the coin 500 times instead of 50 would give an experimental probability much closer to

0.5

. Analyse whether this claim is likely to be correct, using the idea of variability. [1]

Solutions

14QuestionCalculating Combined Probabilities BasicAssessment Practice

5 marks~8 minCriterion B

A game uses two spinners. Spinner X has 3 equal sections labelled A, B, and C. Spinner Y has 2 equal sections labelled 1 and 2. Both spinners are spun at the same time, and all outcomes are equally likely.

List all possible outcomes when both spinners are spun together. [1]

Explain why the total number of outcomes can be found by multiplying the number of sections on each spinner, and write this as a rule using

m

and

n

. [2]

Spinner X is changed to one with 4 equal sections labelled A, B, C, and D. Spinner Y stays the same. Calculate the probability that the result is not (A, 1). [2]

Solutions

15QuestionCalculating Combined Probabilities BasicAssessment Practice

6 marks~9 minCriterion D

A board game designer claims the probability of rolling a 6 twice in a row on a fair die is

\dfrac{1}{36}

. A player suspects their die may be unbalanced from manufacturing or use.

Calculate the theoretical probability of rolling two 6s in a row on a fair die. [2]

Explain how one manufacturing defect and one type of wear could each cause the actual probability to differ from

\dfrac{1}{36}

. [2]

The designer tests the die by rolling it 360 times. The number 6 appears 75 times. Analyse whether this result supports or challenges the claim that the die is fair. [2]

Solutions

16QuestionProbability of a Single Event OccurringAssessment Practice

6 marks~9 minCriterion C

A bag contains 10 red, 6 blue, and 4 green marbles. A student claims: "Red is twice as likely as blue, and blue is 1.5 times as likely as green."

Calculate the probability of selecting each colour. Express each as a fraction in simplest form, a decimal, and a percentage. [2]

Explain how a bar model or probability scale showing all three probabilities supports or challenges the student's claim. [2]

Justify whether the student's claim is correct by testing each part mathematically. [2]

Solutions

17QuestionCreating Fair and Biased ModelsAssessment Practice

6 marks~9 minCriterion D

A school raffle sells 100 tickets. The principal accidentally tears 20 tickets in half. All torn halves and the remaining intact tickets are placed into one bag. A single piece is drawn at random.

Calculate the probability that a student holding one intact ticket wins the raffle. State one assumption you make. [2]

Explain how physical differences between torn and intact pieces could make this raffle unfair. [2]

Analyse how well the probability model from part (a) can be used to predict the outcome of this raffle. Refer to its assumptions and limitations. [2]

Solutions

18QuestionCreating Fair and Biased ModelsAssessment Practice

6 marks~9 minCriterion C

Spinner A has 6 equal sectors labelled 1–6. Spinner B has sectors labelled 1–6, but sectors 1, 2, and 3 are each twice as wide as sectors 4, 5, and 6.

A student claims: "Both spinners are fair because they both show the numbers 1 to 6."

State the condition that must be met for a spinner to be fair. [1]

Calculate

P(1)

for Spinner A and

P(1)

for Spinner B. Show your working. [3]

Explain whether the student's claim is correct, using your results from part (b). [2]

Solutions

19QuestionUsing 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.

Calculate the number of students who like neither sport. [2]

Explain one reason why a Venn diagram may misrepresent survey data that contains errors or inconsistencies. [2]

Solutions

20QuestionCalculating 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.

Construct a tree diagram showing all possible outcomes for two spins, labelling each branch with its probability. [2]

Calculate the probability that the contestant wins a prize on both spins. Show your working. [2]

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

21QuestionDescribing Events as Likely or UnlikelyAssessment Practice

6 marks~9 minCriterion D

A weather forecaster says: "There is a 70% chance of rain tomorrow."

Write

70\%

as a decimal. Then place the event "rain tomorrow" on a probability scale from 0 to 1, using one of the terms: impossible, unlikely, equally likely, likely, or certain. [2]

Explain one advantage and one limitation of using a single percentage to communicate the chance of rain to the public. [2]

A school is deciding whether to hold its sports day outdoors tomorrow. Analyse how the 70% forecast might affect their decision, and whether the percentage alone gives them enough information to plan. [2]

Solutions

22QuestionProbability Scale from 0 to 1Assessment Practice

5 marks~8 minCriterion C

A spinner has 8 equal sections: 3 red, 2 blue, 2 green, and 1 yellow. A student says: "The probability of landing on red is

\dfrac{3}{8}

, so it is likely but not certain."

Calculate the probability of landing on red as a fraction. [1]

Describe where

P(\text{red})

sits on the probability scale from 0 to 1, using the terms unlikely, even chance, or likely. [2]

Explain whether the student's statement is correct, identifying the misconception in their reasoning. [2]

Solutions

23QuestionDrawing Sample Space DiagramsAssessment Practice

2 marks~3 minCriterion D

A school canteen offers three sandwiches (chicken, cheese, veggie) and two drinks (juice, water). A sample space diagram is drawn to show all possible lunch combinations.

Explain one real-world limitation of using a sample space diagram to represent the lunch combinations a student might actually choose. [2]

Solutions

24QuestionCounting Outcomes for Combined EventsAssessment Practice

6 marks~9 minCriterion C

A restaurant offers 3 starters, 4 mains, and 2 desserts. A three-course meal consists of one choice from each course.

Calculate the total number of different three-course meals possible. [2]

The chef removes 2 starters and 1 main from the menu. Calculate the number of different three-course meals now available. [2]

A customer claims the multiplication principle always gives the correct number of meal combinations. Analyse this claim, using the results from parts (a) and (b) to support your reasoning. [2]

Solutions