Simple Probability with Equally Likely Outcomes
When all outcomes are equally likely, probability is found by comparing the number of favorable outcomes to the total number of possible outcomes.
Method
- Identify the sample space: list or count all possible outcomes.
- Count the favorable outcomes: these are the outcomes that match the event asked for.
- Write the probability as
[
P(\text{event}) = \frac{\text{favorable outcomes}}{\text{total outcomes}}
]
- Simplify the fraction to lowest terms.
Example idea
If there are 6 equally likely outcomes and 2 are favorable, the probability is
[
\frac{2}{6} = \frac{1}{3}.
]
Check your answer
- The probability should always be between 0 and 1.
- If the event is impossible, the probability is 0.
- If the event is certain, the probability is 1.
- Make sure your final fraction is simplified.
Helpful habit
For word problems, be careful to count only the outcomes that match the event exactly. If the situation involves a list, spinner, die, cards, or other equally likely results, use the same ratio idea every time: favorable over total.