Rolling a Die
To find the probability of rolling an even number, the favorable outcomes are 2, 4, and 6 out of six possible die results.
P(even) = 3/6 = 1/2
Free Interactive Probability Tool
Basic Probability Practice
Learn probability by identifying favorable outcomes, counting all possible equally likely outcomes, building the probability fraction, simplifying it, and interpreting what the answer means.
Start practicingNeed Help Understanding Basic Probability?
Learn what probability means, how to identify favorable outcomes, how to count equally likely outcomes, how to write probability as a fraction, and how to interpret probabilities from impossible to certain.
Read the Basic Probability Guide
Practice Mode
Work through the full probability process from
favorable outcomes to final interpretation.
Problem 1 of 10
10%
Current Problem
Look at the experiment and identify the outcomes that make the event happen.
Marbles
Full Solution
Beginner
Find the Probability
A bag contains the marbles shown below. What is the probability of choosing a red marble?
Event
Choose a red marble
Favorable Outcomes
?
Total Outcomes
?
Probability
?
Basic Probability
P(event) =
favorable outcomes
total possible outcomes
This counting method works when the outcomes in the sample space are equally likely.
1
Favorable
2
Total
3
Build Fraction
4
Simplify
5
Interpret
Step 1
Count the favorable outcomes
Favorable outcomes are the outcomes that make the event happen. Count how many outcomes in the sample space match the event.
Current Problem
Choose a red marble
Your Work
Find the number of favorable outcomes.
Step 1 of 5
P(event) =
?
?
The numerator counts outcomes that make
the event happen.
Probability Scale
P = ?
0
0.5
1
Impossible
Equally Likely
Certain
Start by counting the outcomes that make the event happen.
Hint
Look only for the outcomes that match the event.
Quick Reference
Basic Probability Reference
Probability Formula
P(event) =
favorable outcomes
total possible outcomes
Favorable Outcomes
Outcomes that satisfy the event you are trying to find.
Sample Space
The complete set of possible outcomes for an experiment.
Probability Range
Every probability is between 0 and 1.
0
0.5
1
Impossible
Equally Likely
Certain
Counting favorable outcomes over total outcomes
assumes that the outcomes are equally likely.
Problem Complete
P(event) = 1/2
There are 3 favorable outcomes out of 6 total equally likely outcomes, so the probability is 3/6 = 1/2 = 0.5 = 50%.
Problems Solved
0
Correct Steps
0
Incorrect Attempts
0
Current Streak
0
Round Complete
Great job!
Problems Solved
10
Correct Steps
0
Incorrect Attempts
0
Accuracy
0%
How Basic Probability Works
Probability compares favorable outcomes with all possible outcomes
When outcomes are equally likely, basic probability can be understood by counting how many outcomes make the event happen and comparing that number with the size of the entire sample space.
Choosing a Color
If a bag contains 3 red marbles out of 8 total, then 3 outcomes are favorable when the event is choosing red.
P(red) = 3/8
Flipping a Coin
A fair coin has two equally likely outcomes: heads and tails. One of those outcomes is heads.
P(heads) = 1/2
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