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Study Guide: UK K12 GCSE/A-Level: Year 8 KS3 Mathematics - Probability, Theoretical and Experimental
Source: https://www.fatskills.com/key-stage-3-ks3/chapter/uk-k12-gcse-a-level-year-8-ks3-mathematics-probability-theoretical-and-experimental

UK K12 GCSE/A-Level: Year 8 KS3 Mathematics - Probability, Theoretical and Experimental

By Fatskills Exam Guides Team — the exam nerds behind 28,500+ quizzes and 2.1M practice questions across 500+ global exams.

⏱️ ~5 min read

Learning Objectives

By the end of this topic, students will be able to:

  • Define probability and explain its importance in real-life situations
  • Distinguish between theoretical and experimental probability
  • Calculate theoretical probability using the formula P(event) = Number of favourable outcomes / Total number of outcomes
  • Conduct experiments to estimate experimental probability and compare it to theoretical probability
  • Identify and explain common misconceptions in probability
  • Apply probability concepts to solve problems in real-life contexts

Core Concepts

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Theoretical probability is calculated using the formula P(event) = Number of favourable outcomes / Total number of outcomes. This is a theoretical value that represents the probability of an event occurring, assuming that all outcomes are equally likely.

Experimental probability, on the other hand, is an estimate of the probability of an event occurring based on repeated trials or experiments. It is often used when the number of possible outcomes is too large to count, or when the outcomes are not equally likely.

Worked Examples

Example 1: Theoretical Probability

A bag contains 5 red marbles and 3 blue marbles. What is the probability of drawing a red marble?

Solution: The number of favourable outcomes (red marbles) is 5, and the total number of outcomes (marbles) is 8. Using the formula P(event) = Number of favourable outcomes / Total number of outcomes, we get P(red) = 5/8 = 0.625.

Example 2: Experimental Probability

A coin is flipped 10 times, and it lands heads up 6 times. What is the experimental probability of the coin landing heads up?

Solution: The number of favourable outcomes (heads) is 6, and the total number of trials is 10. The experimental probability is 6/10 = 0.6.

Common Misconceptions

One common misconception in probability is that the probability of an event occurring is the same as the number of times it has occurred in the past. This is not true, as probability is a measure of the likelihood of an event occurring, not a count of past events.

Another misconception is that the probability of an event occurring is the same as the probability of it not occurring. This is not true, as the probability of an event occurring and the probability of it not occurring are complementary events, and their probabilities add up to 1.

Exam Tips

When answering probability questions, make sure to:

  • Read the question carefully and identify what is being asked
  • Use the formula P(event) = Number of favourable outcomes / Total number of outcomes to calculate theoretical probability
  • Estimate experimental probability based on repeated trials or experiments
  • Identify and explain common misconceptions in probability
  • Use real-life examples to illustrate probability concepts

MCQs with Explanations

MCQ 1 [F]

What is the probability of drawing a red marble from a bag containing 5 red marbles and 3 blue marbles?

A) 1/2 B) 2/3 C) 5/8 D) 3/4

Correct answer: C) 5/8

Why the distractors fail: A) 1/2 is the probability of drawing a red marble from a bag containing an equal number of red and blue marbles. B) 2/3 is the probability of drawing a red marble from a bag containing 2 red marbles and 3 blue marbles. D) 3/4 is the probability of drawing a red marble from a bag containing 3 red marbles and 1 blue marble.

MCQ 2 [H]

A coin is flipped 10 times, and it lands heads up 6 times. What is the experimental probability of the coin landing heads up?

A) 0.4 B) 0.5 C) 0.6 D) 0.7

Correct answer: C) 0.6

Why the distractors fail: A) 0.4 is the probability of the coin landing heads up if it lands tails up 4 times. B) 0.5 is the probability of the coin landing heads up if it is a fair coin. D) 0.7 is the probability of the coin landing heads up if it lands heads up 7 times.

MCQ 3 [F]

What is the probability of drawing a blue marble from a bag containing 5 red marbles and 3 blue marbles?

A) 1/2 B) 2/3 C) 3/8 D) 5/8

Correct answer: C) 3/8

Why the distractors fail: A) 1/2 is the probability of drawing a red marble from a bag containing an equal number of red and blue marbles. B) 2/3 is the probability of drawing a red marble from a bag containing 2 red marbles and 3 blue marbles. D) 5/8 is the probability of drawing a red marble from a bag containing 5 red marbles and 3 blue marbles.

MCQ 4 [H]

A die is rolled, and it lands on an even number 3 times in 5 trials. What is the experimental probability of the die landing on an even number?

A) 0.2 B) 0.4 C) 0.6 D) 0.8

Correct answer: B) 0.6

Why the distractors fail: A) 0.2 is the probability of the die landing on an even number if it lands on an odd number 2 times. B) 0.4 is the probability of the die landing on an even number if it lands on an even number 3 times in 5 trials. D) 0.8 is the probability of the die landing on an even number if it lands on an even number 4 times.

MCQ 5 [F]

What is the probability of drawing a red marble from a bag containing 2 red marbles and 3 blue marbles?

A) 1/2 B) 2/3 C) 1/3 D) 3/5

Correct answer: B) 2/3

Why the distractors fail: A) 1/2 is the probability of drawing a red marble from a bag containing an equal number of red and blue marbles. C) 1/3 is the probability of drawing a red marble from a bag containing 1 red marble and 2 blue marbles. D) 3/5 is the probability of drawing a red marble from a bag containing 3 red marbles and 2 blue marbles.

Short-answer Questions

Question 1

A bag contains 5 red marbles and 3 blue marbles. What is the probability of drawing a red marble?

Question 2

A coin is flipped 10 times, and it lands heads up 6 times. What is the experimental probability of the coin landing heads up?

Question 3

A die is rolled, and it lands on an even number 3 times in 5 trials. What is the experimental probability of the die landing on an even number?

Question 4

A bag contains 2 red marbles and 3 blue marbles. What is the probability of drawing a blue marble?

Question 5

A coin is flipped 5 times, and it lands heads up 3 times. What is the experimental probability of the coin landing heads up?