In probability, all possible outcomes of an experiment together make up the whole set of outcomes. The total probability of all these outcomes is always 1.

 

 

What This Means

An experiment is an action with uncertain results, such as rolling a die or picking a card.

 

The possible outcomes are all the results that could happen.

 

Because one of these outcomes must occur, the probabilities of all possible outcomes added together equal 1.

 

This represents complete certainty that something will happen.

 

 

Total Probability Rule

The total probability rule states:

\( probability\ of\ all\ outcomes = 1 \)

 

This applies to:
• equally likely outcomes
• outcomes with different probabilities
• simple and complex experiments

 

If all outcomes are listed correctly, their probabilities must add to 1.

 

 

Using Fractions, Decimals or Percentages

The rule works in any probability format.

 

Using fractions, the probabilities add to:

\( 1 \)

 

Using decimals, the probabilities add to:

\( 1.0 \)

 

Using percentages, the probabilities add to:

\( 100\% \)

 

All three represent the same total certainty.

 

 

Missing Probability

If the probabilities of some outcomes are known, the remaining probability can be found by subtracting from 1.

 

This works because the total must always equal 1.

 

For example, if the probability of one outcome is known, the probability of all other outcomes combined is whatever is left to make the total equal 1.

 

If probabilities do not add to 1, something is missing or incorrect

 

 

Common Errors to Avoid

Common mistakes include:
• probabilities adding to more than 1
• probabilities adding to less than 1
• forgetting to include all possible outcomes
• mixing probability formats without converting

 

Always check totals carefully.

 

 

Key Points to Remember

All possible outcomes together have a total probability of 1.
This represents complete certainty that one outcome will occur.
The rule applies to fractions, decimals and percentages.
Probabilities must always add up correctly.
Missing probabilities can be found using this rule.

 

Understanding that the total probability of all possible outcomes is 1 is fundamental to working confidently and correctly with probability.