Statistics and Probability · StudentHub Lesson

Probability Basics

Calculate the probability of simple events as favourable outcomes over total outcomes.

18 minBeginner
01

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
02

Watch the lesson

Probability explained | Independent and dependent events · Khan Academy

Watch on YouTube
03

Topic 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
04

Key concepts

Probability formulaSample spaceEqually likely outcomesProbability scale 0 to 1Fraction/decimal/percent forms
05

Important terms

Event
A specific outcome or group of outcomes.
Sample space
All possible outcomes of an experiment.
Fair
Describes equally likely outcomes.
06

Worked examples

Problem

Find the probability of rolling an even number on a fair 6-sided die

  1. 1. Favourable outcomes: 2, 4, 6 (3 outcomes)
  2. 2. Total outcomes: 6
  3. 3. P = 3/6

Answer: 1/2

Problem

Find the probability of drawing a red card from a standard deck

  1. 1. Favourable outcomes: 26 red cards
  2. 2. Total outcomes: 52 cards
  3. 3. P = 26/52

Answer: 1/2

07

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
08

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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