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Statistics & Probability · Foundation & Higher

Mutually exclusive & independent events

Two events are mutually exclusive if they cannot happen at the same time. They are independent if one occurring does not affect the probability of the other.

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Key facts to remember

  • 1Mutually exclusive: P(A and B) = 0.
  • 2For mutually exclusive events: P(A or B) = P(A) + P(B).
  • 3Exhaustive events: their probabilities sum to 1.
  • 4Independent events: P(A and B) = P(A) × P(B).
  • 5Rolling a die and tossing a coin are independent.
  • 6Drawing cards without replacement makes events dependent.
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Worked examples

Example 1

A spinner is red with P(R) = 0.3, blue P(B) = 0.45, green P(G) = ?. Find P(G) and P(R or B).

Working

  1. Probabilities sum to 1: P(G) = 1 − 0.3 − 0.45 = 0.25.
  2. P(R or B) = 0.3 + 0.45 = 0.75.
AnswerP(G) = 0.25, P(R or B) = 0.75
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Common mistakes

✗Assuming events are independent when they are not.
✗Adding probabilities for events that are not mutually exclusive.
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Exam tips

✓"Or" and mutually exclusive → add. "And" and independent → multiply.
✓Always check whether events can overlap before using the OR rule.

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