Basic Probability Formula
Calculate probability with P(A) = favorable outcomes / total outcomes.
The foundation of all probability and statistics.
The Formula
P(A) = Number of Favorable Outcomes / Total Number of Outcomes
Probability measures the likelihood that an event will occur. The result is always between 0 (impossible) and 1 (certain). Multiply by 100 to express it as a percentage.
Variables
| Symbol | Meaning |
|---|---|
| P(A) | Probability of event A occurring |
| Favorable Outcomes | The number of ways the desired event can happen |
| Total Outcomes | The total number of possible outcomes |
Example 1
What is the probability of rolling a 4 on a standard six-sided die?
Favorable outcomes = 1 (only one face shows 4)
Total outcomes = 6 (the die has 6 faces)
P(4) = 1 / 6
P(4) = 0.1667 or about 16.7%
Example 2
A bag has 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of picking a blue marble?
Favorable outcomes = 3 (three blue marbles)
Total outcomes = 5 + 3 + 2 = 10 marbles
P(blue) = 3 / 10
P(blue) = 0.30 or 30%
When to Use It
Use the probability formula when:
- Calculating the chance of a specific outcome in games or experiments
- Making decisions based on likelihood (risk assessment)
- Understanding the foundation before moving to advanced probability topics
- Working with equally likely outcomes (fair dice, coins, card draws)