Key takeaways
- Probability = favorable outcomes ÷ total outcomes, when every outcome is equally likely.
- A probability is always between 0 (impossible) and 1 (certain).
- Multiply by 100 to turn a probability into a percentage.
- Two possible outcomes does not mean a 50% chance unless they are equally likely.
In this guide
What is probability?
When you roll a normal die, six results are possible: 1, 2, 3, 4, 5 or 6. If you want a 6, only one of those results is good for you. So the chance of rolling a 6 is 1 out of 6. That is probability: a number that says how likely something is.
You can write it as a fraction (1/6), a decimal (about 0.167) or a percentage (about 16.7%). All three mean the same thing.
Why does probability matter?
We make choices under uncertainty every day: taking an umbrella, buying a raffle ticket, choosing a route to avoid traffic. Probability turns a vague feeling like 'probably' into a number you can compare.
Rain or no rain is two outcomes, but a 50% chance of rain is only true if both are equally likely. Most mistakes in probability come from forgetting this.
The formula
| Symbol | What it means | Example |
|---|---|---|
| P(A) | The probability of event A | 0.0769 |
| Favorable outcomes | Results where A happens | 4 aces |
| Total outcomes | All possible results | 52 cards |
The favorable number can never be bigger than the total, so the answer is always between 0 and 1. The calculator gives an error if favorable is larger than total or if the total is 0.
How to calculate probability step by step
- 1Count all possible outcomes. This is the total.
- 2Count the favorable outcomes. Only count the ones that match your event.
- 3Divide. Favorable ÷ total gives a decimal between 0 and 1.
- 4Convert if needed. Multiply by 100 for a percentage.
Try it with your own numbers in the calculator below.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Favorable bigger than total. That is impossible. A probability is never more than 1.
- Double counting. In a deck of cards, the ace of hearts is both an ace and a heart. Count it once.
- Using it for several tries at once. For exactly k successes in n tries, use the binomial probability calculator.
- Forgetting that P can be 0. If there are no favorable outcomes, the event is impossible and P = 0.
Tips and tricks
- Estimate first. 4 out of 52 is close to 4 out of 50, so about 8%. The exact answer is about 7.7%.
- Big totals? Use the combinations calculator or the permutations calculator to count them.
- Simplify the fraction. 4/52 is the same as 1/13, which is easier to remember.
Where you'll use it in real life
- Games: dice, cards and board games.
- Weather: a 30% chance of rain means rain on about 3 of every 10 days like this one.
- Lucky draws: 5 tickets out of 500 gives a 1% chance.
- Quality checks: the chance that a randomly picked item from a box is faulty.
Quick summary
To find a probability, divide the number of favorable outcomes by the total number of equally likely outcomes. The answer is between 0 and 1, and times 100 it becomes a percentage. Use the calculator above to check your answer with every step shown.
Worked example
You pick one card at random from a standard 52-card deck. There are 4 aces in the deck. What is the probability that your card is an ace?
- 01P(A) = 4 ÷ 52
- 02P(A) = 0.077
- 03P(A) = 7.69%
These numbers are pre-filled in the calculator above.
Frequently asked questions
What is the probability of rolling a 6 on a die?
There is 1 favorable outcome out of 6, so the probability is 1/6 ≈ 0.167, or about 16.7%.
Can probability be more than 1?
No. A probability is always between 0 and 1 (0% to 100%). A value of 1 means the event is certain.
How do I turn a probability into a percentage?
Multiply the decimal by 100. For example, 4 ÷ 52 ≈ 0.077, which is about 7.7%.
What is the probability of drawing a heart from a deck?
There are 13 hearts in 52 cards, so the probability is 13 ÷ 52 = 0.25, or 25%.
