GCSE Maths Practice: mutually-exclusive-events

Question 7 of 10

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

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\( \begin{array}{l}\textbf{Event M has probability } \frac{1}{3}, \text{ and Event N has probability } \frac{1}{4}. \\ \text{The events are mutually exclusive.} \\ \text{Find the probability of M or N.}\end{array} \)

Choose one option:

Confirm that the events cannot overlap before adding their probabilities.

Mutually Exclusive Events Explained Clearly

In GCSE probability, one of the first relationships students learn about is when events are mutually exclusive. Two events are mutually exclusive if they cannot happen at the same time. If one event occurs, the other event is guaranteed not to occur.

This idea is important because it tells you exactly which probability rule to use. When events are mutually exclusive, there is no overlap between them, so each outcome is counted only once.

The Addition Rule

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

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

This rule works because the events do not share any outcomes.

Worked Example 1

A fair spinner is divided into 6 equal sections.

  • The probability of landing on section 1 is \( \frac{1}{6} \).
  • The probability of landing on section 4 is \( \frac{1}{6} \).

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 probabilities.

Worked Example 2

A bag contains cards numbered from 1 to 5.

  • The probability of picking card number 2 is \( \frac{1}{5} \).
  • The probability of picking card number 5 is \( \frac{1}{5} \).

Only one card is selected, so it cannot be both numbers at once. These events are mutually exclusive, allowing the probabilities to be added.

Common Mistakes

  • Adding probabilities when events overlap: If two events can happen together, simple addition is not correct.
  • Missing key words: Phrases such as “either”, “only one”, or “cannot happen together” often signal mutually exclusive events.
  • Confusing ‘or’ and ‘and’: The addition rule applies to “or”, not “and”.

Real-Life Examples

Mutually exclusive events appear often in everyday situations. When choosing a single option from a menu, you may choose tea or coffee, but not both at the same time. In games, a player may win or lose, but cannot do both simultaneously.

These examples help show why probabilities can be added in these situations.

Frequently Asked Questions

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

Can the total probability ever be greater than 1?
No. Probabilities represent chances, so the total cannot exceed 1.

Why is this topic important?
It forms the foundation for more advanced probability topics later in GCSE Maths.

Study Tip

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

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