How do I calculate the probability of a single event?

Divide the number of favorable outcomes by the total number of equally likely outcomes. Rolling a six on a fair die is 1 favorable outcome out of 6 total, so the probability is 1/6 ≈ 0.1667, or about 16.67%. This classical definition only holds when every outcome is equally likely, which is true for fair dice, coins, and well-shuffled cards.

What is the difference between probability and odds?

Probability compares favorable outcomes to all outcomes, while odds compare favorable outcomes to unfavorable ones. A probability of 1/6 corresponds to odds of 1:5 for the event and 5:1 against it. Bookmakers and everyday speech usually quote odds, while science and statistics work with probabilities, so converting between them is a common need this tool handles automatically.

When do I multiply probabilities and when do I add them?

Multiply for “and” when the events are independent: P(A and B) = P(A) × P(B), like two coin flips both landing heads. Add for “or” — but subtract the overlap: P(A or B) = P(A) + P(B) − P(A and B). If the events are mutually exclusive they cannot happen together, so the overlap is zero and you simply add. The calculator applies the correct formula for the relationship you select and shows each step.

How does the “at least once” formula work?

The chance of at least one success in n independent trials is 1 minus the chance of failing every time: 1 − (1 − p)ⁿ. With a 10% chance per trial and 10 trials, that is 1 − 0.9¹⁰ ≈ 65.1% — notably not 100%, a common misconception. The formula assumes each trial is independent with the same success probability, which fits dice rolls, loot drops, and repeated random draws with replacement.

Is anything I enter sent to a server?

No. All three calculators run entirely in your browser with plain JavaScript, and nothing you type leaves your device. There is no account, no upload, and no tracking of your inputs, and the page keeps working offline once it has loaded, so you can use it for homework, betting analysis, or work without any privacy concerns.

Probability Calculator

Work out the probability of a single event, combine two events, or find the chance of at least one success in repeated trials — every result shows the formula behind it.

1. Single event

Probability of one event from favorable and total outcomes.

Favorable outcomesTotal outcomes

Probability

16.67%

P = 1 / 6 = 0.1667

Odds for

1 : 5

Odds against

5 : 1

2. Two events

Combine two events. Enter probabilities as decimals between 0 and 1.

P(A)P(B)

Relationship

P(A and B)

0.15 (15%)

P(A) × P(B) = 0.5 × 0.3 = 0.15

P(A or B)

0.65 (65%)

P(A) + P(B) − P(A)P(B) = 0.5 + 0.3 − 0.15 = 0.65

P(not A)

0.5 (50%)

1 − P(A) = 1 − 0.5 = 0.5

3. At least once in n trials

Chance of succeeding at least once across repeated independent trials.

Probability per trialNumber of trials

Probability of at least one success

65.13%

1 − (1 − 0.1)¹⁰ = 1 − 0.3487 = 0.6513

Probability of no success at all: 34.87%

Formulas assume equally likely outcomes and independent trials where stated. Calculated on your device; nothing is sent anywhere.

How it works

For a single event, enter the number of favorable outcomes and the total number of possible outcomes to get the probability, percentage, and odds for and against.
For two events, enter P(A) and P(B) as decimals between 0 and 1, then choose whether the events are independent or mutually exclusive to get P(A and B), P(A or B), and P(not A).
For repeated trials, enter the probability of success in one trial and the number of trials to see the chance of succeeding at least once, calculated as 1 − (1 − p)ⁿ.

Frequently asked questions

How do I calculate the probability of a single event?: Divide the number of favorable outcomes by the total number of equally likely outcomes. Rolling a six on a fair die is 1 favorable outcome out of 6 total, so the probability is 1/6 ≈ 0.1667, or about 16.67%. This classical definition only holds when every outcome is equally likely, which is true for fair dice, coins, and well-shuffled cards.
What is the difference between probability and odds?: Probability compares favorable outcomes to all outcomes, while odds compare favorable outcomes to unfavorable ones. A probability of 1/6 corresponds to odds of 1:5 for the event and 5:1 against it. Bookmakers and everyday speech usually quote odds, while science and statistics work with probabilities, so converting between them is a common need this tool handles automatically.
When do I multiply probabilities and when do I add them?: Multiply for “and” when the events are independent: P(A and B) = P(A) × P(B), like two coin flips both landing heads. Add for “or” — but subtract the overlap: P(A or B) = P(A) + P(B) − P(A and B). If the events are mutually exclusive they cannot happen together, so the overlap is zero and you simply add. The calculator applies the correct formula for the relationship you select and shows each step.
How does the “at least once” formula work?: The chance of at least one success in n independent trials is 1 minus the chance of failing every time: 1 − (1 − p)ⁿ. With a 10% chance per trial and 10 trials, that is 1 − 0.9¹⁰ ≈ 65.1% — notably not 100%, a common misconception. The formula assumes each trial is independent with the same success probability, which fits dice rolls, loot drops, and repeated random draws with replacement.
Is anything I enter sent to a server?: No. All three calculators run entirely in your browser with plain JavaScript, and nothing you type leaves your device. There is no account, no upload, and no tracking of your inputs, and the page keeps working offline once it has loaded, so you can use it for homework, betting analysis, or work without any privacy concerns.

About this tool

This probability calculator bundles the three computations people reach for most often into one page. The first section handles a single event: enter favorable and total outcomes and it returns the probability as a fraction, a decimal, and a percentage, plus the odds for and against the event in simplified form. The second combines two events: given P(A) and P(B), it computes P(A and B), P(A or B), and P(not A), using the correct rule for independent or mutually exclusive events. The third answers the question “what is the chance this happens at least once if I try n times?” using the complement rule 1 − (1 − p)ⁿ.

Every result is shown together with the formula and the substituted numbers, so you can see exactly how the answer was reached rather than trusting a black box. That makes the tool useful for checking homework step by step, not just getting a final number. All arithmetic runs locally in your browser — nothing you enter is transmitted anywhere — and results update live as you type.

Typical uses include probability and statistics coursework, working out dice and card odds for board games, estimating the chance of a rare drop across many attempts in a video game, quick risk calculations such as the likelihood of at least one failure across independent components, and converting between the odds format used in betting and the probabilities used in analysis.

A few practical tips: enter probabilities in the second and third sections as decimals between 0 and 1 (50% is 0.5). Remember that the independence assumption matters — drawing cards without replacement makes events dependent, and the simple product rule no longer applies. And for the “at least once” section, note how slowly the probability approaches 100%: a 1% event over 100 trials succeeds at least once only about 63% of the time.