When working with probability, it is essential to recognise whether probabilities should be added or multiplied. This depends on the relationship between the events and the wording of the question.

 

 

Understanding the Two Situations

There are two common situations:

• events that cannot happen at the same time
• events that do not affect each other

 

Each situation uses a different rule.

 

 

Mutually Exclusive Events

Events are mutually exclusive if they cannot occur together in the same experiment.

 

If one event happens, the other cannot happen.

 

Key wording clues include:
• “A or B”
• “either A or B”

 

When events are mutually exclusive and the question asks for A or B, probabilities are added.

 

This rule is written as:

\( P(A\ or\ B) = P(A) + P(B) \)

 

You add probabilities because there is no overlap between the events.

 

Use addition only when events cannot happen together

 

 

Independent Events

Events are independent if the outcome of one does not affect the outcome of the other.

 

Key wording clues include:
• “A and B”
• “both A and B”

 

When events are independent and the question asks for A and B, probabilities are multiplied.

 

This rule is written as:

\( P(A\ and\ B) = P(A) \times P(B) \)

 

You multiply probabilities because both events must occur.

 

Use multiplication when events are independent and both must happen

 

 

How to Decide Which Rule to Use

To decide whether to add or multiply:

 

First, ask:
• Can the events happen at the same time?

 

If no, they are mutually exclusive and you add.

 

Then ask:
• Does one event affect the probability of the other?

 

If no, they are independent and you multiply.

 

The word or usually signals addition.
The word and usually signals multiplication.

 

Context and event relationship matter more than keywords

 

 

Common Errors to Avoid

Common mistakes include:
• adding probabilities for independent events
• multiplying probabilities for mutually exclusive events
• assuming events are independent without checking
• ignoring whether events can overlap

 

Always identify the type of events before choosing a rule.

 

 

Key Points to Remember

Mutually exclusive events cannot occur together.
For mutually exclusive events, probabilities are added.
Independent events do not affect each other.
For independent events, probabilities are multiplied.
Always check the relationship between events before calculating.

 

Recognising when to add or multiply probabilities ensures probability calculations are correct and logically sound.