Probability Calculator Formula
Understand the math behind the probability calculator. Each variable explained with a worked example.
Formulas Used
Probability
probability = favorable / totalProbability (%)
percentage = (favorable / total) * 100Odds in Favor
odds_for = favorable / (total - favorable)Variables
| Variable | Description | Default |
|---|---|---|
favorable | Favorable Outcomes | 3 |
total | Total Outcomes | 10 |
How It Works
How to Calculate Probability
Formula
P(A) = Favorable outcomes / Total outcomes
Probability measures how likely an event is to occur, ranging from 0 (impossible) to 1 (certain). Multiply by 100 to express as a percentage. The odds in favor are the ratio of favorable to unfavorable outcomes.
Worked Example
A bag has 3 red balls out of 10 total. What is the probability of drawing a red ball?
- 01Favorable outcomes = 3 (red balls)
- 02Total outcomes = 10 (all balls)
- 03P(red) = 3 / 10 = 0.3
- 04As a percentage: 0.3 * 100 = 30%
- 05Odds in favor: 3 / (10 - 3) = 3/7 ≈ 0.4286
Frequently Asked Questions
What is the range of probability?
Probability always falls between 0 and 1, inclusive. A probability of 0 means the event is impossible, while 1 means it is certain.
How do I convert probability to odds?
Odds in favor = P / (1 - P). For example, a probability of 0.25 gives odds of 0.25 / 0.75 = 1/3, or "1 to 3".
What is the difference between theoretical and experimental probability?
Theoretical probability is computed from known outcomes (like dice), while experimental probability is estimated from observed data. As trials increase, experimental probability approaches theoretical probability (law of large numbers).
Ready to run the numbers?
Open Probability Calculator