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Statistics & Probability · Foundation & Higher

Basic probability

Probability measures how likely an event is to occur, on a scale from 0 (impossible) to 1 (certain).

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Key facts to remember

  • 1P(event) = number of favourable outcomes ÷ total number of equally likely outcomes.
  • 2Probabilities range from 0 to 1.
  • 3P(event does not happen) = 1 − P(event happens). This is the complementary rule.
  • 4If events are mutually exclusive: P(A or B) = P(A) + P(B).
  • 5If events are independent: P(A and B) = P(A) × P(B).
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Formulas

Basic probability
P(A) = favourable outcomes ÷ total outcomes
Complement
P(A') = 1 − P(A)
Independent events
P(A and B) = P(A) × P(B)
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Worked examples

Example 1

A bag has 3 red, 5 blue and 2 green balls. Find P(red) and P(not green).

Working

  1. Total = 3 + 5 + 2 = 10
  2. P(red) = 3/10
  3. P(green) = 2/10 = 1/5
  4. P(not green) = 1 − 1/5 = 4/5
AnswerP(red) = 3/10, P(not green) = 4/5
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Common mistakes

✗Forgetting to count the total number of outcomes.
✗Adding probabilities when you should multiply (for "and" use ×, for mutually exclusive "or" use +).
✗Not simplifying fractions.
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Exam tips

✓Always check probabilities add up to 1 for a complete set of outcomes.
✓Use fractions or decimals — never write "3 in 10" as a final answer without a proper fraction/decimal.

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