Statistics and Probability · StudentHub Lesson
Probability Basics
Calculate the probability of simple events as favourable outcomes over total outcomes.
What you will learn
- Define the probability of an event
- Express probability as a fraction, decimal or percentage
- Calculate probability from favourable and total outcomes
- Understand the probability scale from 0 to 1
- Apply probability to coin and dice examples
Watch the lesson
Probability explained | Independent and dependent events · Khan Academy
Watch on YouTubeTopic notes
Main Idea
Probability measures how likely an event is to happen, expressed as a number between 0 (impossible) and 1 (certain).
Key Concepts
- Probability = number of favourable outcomes / total number of possible outcomes
- A fair coin or die has equally likely outcomes
- Probabilities can be written as fractions, decimals or percentages
Definitions
- Event: an outcome or set of outcomes we are interested in
- Sample space: the set of all possible outcomes
- Fair: all outcomes equally likely
Formulas
- P(event) = favourable outcomes / total outcomes
- 0 ≤ P(event) ≤ 1
Examples
- Probability of rolling a 4 on a fair die: 1/6
- Probability of flipping heads on a fair coin: 1/2
Common Mistakes
- Not counting all possible outcomes correctly
- Confusing probability with odds
- Writing probability greater than 1 or less than 0
Key concepts
Important terms
- Event
- A specific outcome or group of outcomes.
- Sample space
- All possible outcomes of an experiment.
- Fair
- Describes equally likely outcomes.
Worked examples
Problem
Find the probability of rolling an even number on a fair 6-sided die
- 1. Favourable outcomes: 2, 4, 6 (3 outcomes)
- 2. Total outcomes: 6
- 3. P = 3/6
Answer: 1/2
Problem
Find the probability of drawing a red card from a standard deck
- 1. Favourable outcomes: 26 red cards
- 2. Total outcomes: 52 cards
- 3. P = 26/52
Answer: 1/2
Quick revision
- P = favourable/total
- Probability ranges from 0 to 1
- 0 means impossible, 1 means certain
- Fair means equally likely outcomes
- Can be a fraction, decimal or percent
- The sample space lists all outcomes
Check your understanding
Question 1 · Multiple choice
What is the probability of flipping tails on a fair coin?
Question 2 · Multiple choice
A bag has 3 red and 2 blue balls. What is P(blue)?
Question 3 · Short answer
What is the probability of rolling a 6 on a fair die?
Question 4 · Short answer
A spinner has 4 equal sections: red, blue, green, yellow. What is P(green)?
Question 5 · True or false
Probability values can be greater than 1.
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