Probability
Overview
Probability measures how likely an event is to happen, placing every outcome on a scale from impossible (0) to certain (1). This topic gives you the vocabulary, notation and calculation techniques that underpin risk assessment, game design, weather forecasting and medical testing.
You will learn to list outcomes systematically, calculate theoretical and experimental probabilities, combine events using the addition rule for mutually exclusive outcomes, and read probabilities from Venn diagrams. Higher-tier students extend these ideas to tree diagrams, independent events and conditional probability.
Objectives
- Understand the language of probability
- Understand and use the probability scale
- Understand and use estimates or measures of probability from theoretical models
- Find probabilities from a Venn diagram
- Understand the concepts of a sample space and an event, and how the probability of an event happening can be determined from the sample space
- List all the outcomes for single events and for two successive events in a systematic way
- Estimate probabilities from previously collected data
- Calculate the probability of the complement of an event happening
- Use the addition rule of probability for mutually exclusive events
- Understand and use the term 'expected frequency'
- [Higher] Draw and use tree diagrams
- [Higher] Determine the probability that two or more independent events will occur
- [Higher] Use simple conditional probability when combining events
- [Higher] Apply probability to simple problems
Mind map
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Flashcards
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Probability. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- A fair six-sided die is rolled once. What is the probability of rolling a number greater than 4? A) 1/6 B) 1/3 C) 1/2 D) 2/3 Answer: B
- Events A and B are mutually exclusive. P(A) = 0.3 and P(B) = 0.5. What is P(A or B)? A) 0.15 B) 0.2 C) 0.8 D) 1.0 Answer: C
- The probability of an event happening is 0.35. What is the probability of it not happening? A) 0.35 B) 0.45 C) 0.55 D) 0.65 Answer: D
- A biased spinner lands on red 45 times out of 150 spins. What is the estimated probability of landing on red? A) 45/150 B) 1/3 C) 3/10 D) Both A and C Answer: D
- A bag contains 5 red and 7 blue counters. One counter is drawn at random. What is the probability it is blue? A) 5/12 B) 7/12 C) 5/7 D) 7/5 Answer: B
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Recommended Books
Practice Mock Questions
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