GCSE Maths Practice: mutually-exclusive-events

Question 6 of 10

This question checks your understanding of adding probabilities for mutually exclusive events.

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\( \begin{array}{l}\textbf{Event L has probability } \frac{5}{9}, \text{ and Event K has probability } \frac{2}{9}. \\ \text{The events are mutually exclusive.} \\ \text{Find the probability of L or K.}\end{array} \)

Choose one option:

Confirm that the events cannot happen together before applying the addition rule.

Understanding Mutually Exclusive Events

In probability, it is essential to understand how events are related before choosing a calculation method. Two events are said to be mutually exclusive when they cannot occur at the same time. If one event happens, the other event definitely does not.

This idea appears frequently in GCSE Maths because it provides a clear and simple rule for combining probabilities. When events are mutually exclusive, there is no overlap between them, so outcomes are never counted twice.

The Key Probability Rule

For two mutually exclusive events A and B, the probability that either A or B occurs is given by:

\[ P(A \text{ or } B) = P(A) + P(B) \]

This formula works because the events have no shared outcomes. Each probability represents a separate set of possible results.

Worked Example 1

A fair spinner is divided into 9 equal sections.

  • The probability of landing on section 1 is \( \frac{1}{9} \).
  • The probability of landing on section 4 is \( \frac{1}{9} \).

The spinner can only land on one section at a time, so these events are mutually exclusive. The probability of landing on section 1 or section 4 is found by adding the two probabilities.

Worked Example 2

A bag contains balls of different colours.

  • The probability of selecting a green ball is \( \frac{3}{10} \).
  • The probability of selecting a yellow ball is \( \frac{4}{10} \).

Only one ball is selected, so it cannot be both colours at once. These events are mutually exclusive, and their probabilities can be combined using addition.

Common Mistakes to Avoid

  • Adding probabilities when events overlap: If two events can happen together, the simple addition rule does not apply.
  • Not checking the wording: Phrases like “either”, “only one”, or “cannot occur together” usually indicate mutual exclusivity.
  • Confusing ‘or’ with ‘and’: Mutually exclusive rules apply to “or” statements, not “and”.

Everyday Examples

Mutually exclusive events occur often in everyday situations. For example, when choosing a single dessert, you might choose cake or ice cream, but not both at the same time. In sports, a match might end in a win or a loss, but not both.

Seeing these real-life situations helps students understand why the addition rule makes sense and when it should be used.

Frequently Asked Questions

How do I quickly recognise mutually exclusive events?
Ask whether both events could happen at the same time. If the answer is no, they are mutually exclusive.

Can probabilities ever add up to more than 1?
No. The total probability of all possible outcomes cannot be greater than 1.

Why is this important for GCSE Maths?
This topic is a foundation concept that supports more advanced probability questions later on.

Study Tip

Always identify the relationship between events before calculating. Choosing the correct rule first makes probability questions much easier.

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