Unit 9 · Class 7 IB MYP · MCQ Test
Probability (Experimental) MCQ Test — Class 7 IB MYP
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Probability (Experimental) — MCQ Questions
1A spinner has 8 equally sized sectors labelled 1, 2, 3, 4, 5, 6, 7, 8. What is the theoretical probability of the spinner landing on an odd number?
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Answer: 1/2
Hint: Identify the total number of possible outcomes and the number of outcomes that are odd.
Solution:
Identify the sample space: The numbers are 1, 2, 3, 4, 5, 6, 7, 8. The total number of outcomes is 8.
Identify the favourable outcomes: The odd numbers are 1, 3, 5, 7. There are 4 favourable outcomes.
Calculate the theoretical probability: P(odd) = (Number of odd outcomes) / (Total number of outcomes). — P(odd) = 4 / 8
Simplify the fraction. — P(odd) = 1/2
2A student rolls a standard six-sided die 60 times. The number '4' appears 12 times. What is the experimental probability of rolling a '4'?
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Answer: 1/5
Hint: Experimental probability is calculated from the results of an experiment. How many times did the event occur compared to the total trials?
Solution:
Identify the number of times the event occurred: The number '4' appeared 12 times.
Identify the total number of trials: The die was rolled 60 times.
Calculate the experimental probability: P(4) = (Number of times '4' appeared) / (Total number of rolls). — P(4) = 12 / 60
Simplify the fraction. — P(4) = 1/5
3Which statement best describes the relationship between theoretical probability and experimental probability?
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Answer: Experimental probability becomes closer to theoretical probability as the number of trials increases.
Hint: Think about what happens when you repeat an experiment many, many times. Does the observed frequency stabilize?
Solution:
Evaluate option A: This is false. They are often different, especially with a small number of trials.
Evaluate option B: This is true. The Law of Large Numbers states that as the number of trials increases, the experimental probability (or relative frequency) will tend to get closer to the theoretical probability.
Evaluate option C: This is false. Theoretical probability is for ideal situations (e.g., fair die), and experimental probability comes from real-world experiments.
Evaluate option D: This is false. Experimental probability, by definition, requires an experiment to be conducted to gather data.
4Sarah tossed a coin 20 times. She recorded Heads 8 times and Tails 12 times. She then calculated the experimental probability of getting Heads as 12/20. What mistake did Sarah make?
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Answer: She confused the number of Heads with the number of Tails.
Hint: Carefully read what she was trying to calculate (probability of Heads) and what numbers she used.
Solution:
Identify what Sarah was calculating: The experimental probability of getting Heads.
Identify the number of Heads recorded: Sarah recorded 8 Heads.
Identify the number of Tails recorded: Sarah recorded 12 Tails.
Compare Sarah's calculation (12/20) with the correct value: For Heads, she should have used 8/20. She used the number of Tails instead of Heads. Therefore, she confused the number of Heads with the number of Tails.
5A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If a marble is selected at random, what is the theoretical probability of selecting a blue marble?
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Answer: 3/10
Hint: First, find the total number of marbles. Then, identify how many of them are blue.
Solution:
Calculate the total number of marbles in the bag: 5 (red) + 3 (blue) + 2 (green) = 10 marbles.
Identify the number of favourable outcomes: There are 3 blue marbles.
Calculate the theoretical probability: P(blue) = (Number of blue marbles) / (Total number of marbles). — P(blue) = 3 / 10
6A weather station in Geneva recorded 15 rainy days out of 60 days in a month. Based on this data, what is the experimental probability of rain on any given day in that month?
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Answer: 1/4
Hint: The experimental probability is the ratio of the number of times an event occurred to the total number of trials.
Solution:
Identify the number of rainy days (favourable outcome): 15 days.
Identify the total number of days (total trials): 60 days.
Calculate the experimental probability: P(rain) = (Number of rainy days) / (Total number of days). — P(rain) = 15 / 60
Simplify the fraction. — P(rain) = 1/4
7A café observes that out of 200 customers, 40 ordered coffee. If the café expects 500 customers tomorrow, approximately how many would they expect to order coffee, based on this experimental probability?
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Answer: 100
Hint: First, find the experimental probability of a customer ordering coffee. Then, apply this probability to the new total number of customers.
Solution:
Calculate the experimental probability of a customer ordering coffee: P(coffee) = (Number of customers who ordered coffee) / (Total customers). — P(coffee) = 40 / 200 = 1/5
Use this probability to predict for 500 customers: Expected orders = P(coffee) × Total expected customers. — Expected orders = (1/5) × 500
Calculate the final number. — Expected orders = 100
8A fair coin is tossed, and then a standard six-sided die is rolled. What is the total number of possible outcomes in the sample space for this two-step experiment?
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Answer: 12
Hint: Multiply the number of outcomes for each individual step to find the total number of combined outcomes.
Solution:
Identify the number of outcomes for the first step (coin toss): There are 2 outcomes (Heads, Tails).
Identify the number of outcomes for the second step (die roll): There are 6 outcomes (1, 2, 3, 4, 5, 6).
Calculate the total number of possible outcomes: Multiply the number of outcomes for each step. — Total outcomes = 2 × 6
Perform the multiplication. — Total outcomes = 12
9A tree diagram shows the possible outcomes of selecting a coloured ball (Red or Blue) from a bag, and then flipping a coin (Heads or Tails). How many unique end branches would this tree diagram have?
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Answer: 4
Hint: Each path from the start to an end point represents a unique outcome. Count the number of possible outcomes for each stage and multiply them.
Solution:
Identify the number of outcomes for the first event (selecting a ball): 2 outcomes (Red, Blue).
Identify the number of outcomes for the second event (flipping a coin): 2 outcomes (Heads, Tails).
To find the total number of unique end branches (total possible outcomes), multiply the number of outcomes for each event. — Total branches = 2 × 2
Calculate the total. — Total branches = 4
10A survey of students in Berlin found that the experimental probability of a student walking to school is 3/5. If 300 students were surveyed, how many of them walked to school?
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Answer: 180
Hint: You are given the experimental probability and the total number of trials. Use these to find the number of successful outcomes.
Solution:
Identify the experimental probability: P(walking) = 3/5.
Identify the total number of students surveyed: 300 students.
To find the number of students who walked, multiply the total number of students by the experimental probability. — Number walking = (3/5) × 300
Calculate the result. — Number walking = 180
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Tips for Probability (Experimental) MCQs
- 1Read each question carefully and identify what is being asked before looking at the options.
- 2Try to solve the problem mentally or on paper first, then match your answer with the options.
- 3Use elimination — rule out clearly wrong options to improve your chances even when unsure.
- 4Check units, signs, and edge cases — these are common traps in Probability (Experimental) MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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