What is important to know about Mutually exclusive & independent events?

Mutually exclusive: P(A and B) = 0.

What is important to know about Mutually exclusive & independent events?

For mutually exclusive events: P(A or B) = P(A) + P(B).

What is important to know about Mutually exclusive & independent events?

Exhaustive events: their probabilities sum to 1.

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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

Probabilities sum to 1: P(G) = 1 − 0.3 − 0.45 = 0.25.
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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