Introduction to Probability

2026 What You Need to Know (Syllabus Objectives)

By the end of this topic, you should be able to:

  1. Understand and use the probability scale from 0 to 1
  2. Calculate the probability of a single event
  3. Understand that the probability of an event not occurring = 1 – the probability of the event occurring
  4. Understand and use probability notation: P(A) and P(A')
  5. Give probabilities as fractions, decimals, or percentages
  6. Solve problems using information from tables, graphs, or Venn diagrams

1. What is Probability?

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Probability is the study of chance. It tells us how likely something is to happen.

In everyday life, you might say things like "that's impossible" or "that's certain to happen." In mathematics, we use numbers to describe these chances instead of words.

The Probability Scale:

Every probability is given a number between 0 and 1:

  • 0 means impossible – the event will never happen
  • 1 means certain – the event will definitely happen
  • 0.5 (or ½) means even chance – the event has a 50-50 chance of happening

The scale looks like this:

0 ------------------- 0.5 ------------------- 1
IMPOSSIBLE         EVEN CHANCE           CERTAIN
   ↑                     ↑                    ↑
Unlikely events    Equal chance      Likely events
(between 0-0.5)                     (between 0.5-1)

Examples:

  • The probability that a pig will fly = 0 (impossible)
  • The probability that the sun will rise tomorrow = 1 (certain)
  • The probability that a fair coin lands on heads = 0.5 (even chance)

2. How to Give Your Answer

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Probabilities can be written in three different ways:

  1. As a fraction: ½, ¾, ⅗
  2. As a decimal: 0.5, 0.75, 0.6
  3. As a percentage: 50%, 75%, 60%

All three ways are correct. Unless the question tells you which form to use, fractions are usually best because they are exact and easy to work with.

Example conversions:

  • ½ = 0.5 = 50%
  • ¼ = 0.25 = 25%
  • ⅗ = 0.6 = 60%

3. Calculating the Probability of a Single Event

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To find the probability of something happening, we use this formula:

P(event) = Number of favorable outcomes / Total number of outcomes

Let me break this down:

  • Favorable outcomes = the outcomes you want (the successful results)
  • Total number of outcomes = all the possible results that could happen

Example 1: Tossing a coin

When you toss a fair coin, there are 2 possible outcomes: Heads (H) or Tails (T).

What is the probability of getting heads?

  • Favorable outcomes = 1 (only heads counts)
  • Total outcomes = 2 (heads or tails)
  • P(heads) = 1/2 = 0.5 = 50%

Example 2: Rolling a dice

A standard dice has 6 faces numbered 1, 2, 3, 4, 5, 6.

What is the probability of rolling an even number?

  • Even numbers on a dice = 2, 4, 6 (that's 3 favorable outcomes)
  • Total outcomes = 6
  • P(even) = 3/6 = 1/2 = 0.5

Example 3: Bag of counters

A bag contains 5 blue counters, 3 red counters, and 2 yellow counters.

What is the probability of picking a blue counter?

  • Favorable outcomes = 5 (blue counters)
  • Total outcomes = 5 + 3 + 2 = 10 (all counters)
  • P(blue) = 5/10 = 1/2 = 0.5

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