Theoretical probability is used when all outcomes of an experiment are equally likely. This means each possible outcome has the same chance of occurring. The probability is calculated using reasoning, not data from experiments.

 

 

What Equally Likely Outcomes Means

Outcomes are equally likely if:
• they all have the same chance of happening
• there is no bias in the experiment

 

For example, in a fair coin toss, heads and tails are equally likely.

 

If outcomes are not equally likely, theoretical probability cannot be used directly.

 

Always check that outcomes are equally likely before using this method

 

 

Theoretical Probability Formula

The theoretical probability of an event is calculated using:

\( \frac{number\ of\ favourable\ outcomes}{total\ number\ of\ possible\ outcomes} \)

 

This formula applies only when all outcomes are equally likely.

 

The result must lie between zero and one.

 

 

Calculating Theoretical Probability

To calculate theoretical probability:

• list all possible outcomes
• count the total number of outcomes
• identify the outcomes that satisfy the event
• divide the number of favourable outcomes by the total number of outcomes

 

For example, when rolling a fair six sided die:
• there are 6 possible outcomes
• each outcome is equally likely

 

If the event is rolling an even number, the favourable outcomes are 2, 4 and 6.

 

This gives a probability of:

\( \frac{3}{6} \)

 

This fraction can be simplified if needed.

 

 

Expressing the Probability

The probability can be written as:
• a fraction
• a decimal
• a percentage

 

All three forms represent the same likelihood.

 

Probabilities should always be given in a clear and appropriate form.

 

 

Using Theoretical Probability

Theoretical probability is commonly used for:
• dice
• coins
• spinners with equal sections
• cards from a well shuffled deck

 

It assumes the experiment is fair and unbiased.

 

If the experiment is not fair, experimental probability is more appropriate.

 

 

Common Errors to Avoid

Common mistakes include:
• forgetting to list all possible outcomes
• assuming outcomes are equally likely when they are not
• using incorrect totals
• giving probabilities greater than one

 

Careful counting avoids these errors.

 

 

Key Points to Remember

Theoretical probability is used when outcomes are equally likely.
All possible outcomes must be counted.
The probability is favourable outcomes divided by total outcomes.
The result must lie between zero and one.
Always check that the experiment is fair.

 

Being able to calculate theoretical probabilities correctly allows chance situations to be analysed logically and accurately.