Probability Calculator
Find combined and complement probabilities for two independent events, or a single probability from favorable over total outcomes.
Reviewed by the CalcCafe editorial team · Last updated 1 July 2026 · How we test our tools
Example
With P(A) = 0.5 and P(B) = 0.4 (independent):
P(A and B) = 0.5 x 0.4 = 0.2
P(A or B) = 0.5 + 0.4 - 0.2 = 0.7
P(not A) = 1 - 0.5 = 0.5
Neither = 0.5 x 0.6 = 0.3
Single event: 13 of 52 cards = 13/52 = 0.25 (25%)
How it works
Enter P(A) and P(B) as decimals (0 to 1) to get the intersection, union, and complements assuming independence, or switch to single-event mode and enter favorable and total outcomes.
Good to know
This Probability Calculator handles two distinct jobs from one screen. In "Two events" mode you enter the probabilities of two independent events, P(A) and P(B), each as a decimal between 0 and 1, and it instantly returns the chance both happen, the chance at least one happens, each event's complement, and the chance neither occurs. In "Single event" mode you enter favorable and total outcomes (like 13 face-suit cards out of 52) and it converts that fraction into a decimal probability, a percentage, betting-style odds, and the complement. It is aimed at students working through probability homework, anyone checking a quick "what are the chances" estimate, and people who want odds and percentages without doing the arithmetic by hand.
Reach for two-event mode when your scenarios are independent: two coin flips, two unrelated machines failing, or a hit on two separate attempts. Use single-event mode when you can count outcomes directly, such as drawing a specific card, rolling a value on a die, or pulling one item from a known pool. The single-event odds output (for : against) is handy for translating a probability into the language used in gaming, sports, and risk discussions.
To read the results: every probability is shown rounded to four decimals, so 0.2 means a 20 percent chance and 1 would mean certainty. In two-event mode, "P(A or B)" is always at least as large as either single probability and "Neither" equals 1 minus "P(A or B)" as a built-in cross-check. In single-event mode the percent and odds are just two views of the same fraction, and the complement tells you how often the event does not happen.
One important caveat: the two-event calculation assumes independence and multiplies P(A) by P(B), so it is wrong for events that influence each other, such as drawing two cards without replacement. The calculator also clamps two-event inputs to the 0-to-1 range and, in single-event mode, requires total to be above zero with favorable not exceeding total; if your numbers fall outside those bounds the result simply shows 0 or a dash rather than a misleading value.
Frequently asked questions
Does this assume the two events are independent?
Yes. In two-event mode P(A and B) is calculated as P(A) x P(B), which only holds when A and B are independent. For dependent events you would need the conditional probability P(B given A).
What does the 'Neither' result mean?
Neither is the probability that both events fail to occur, computed as (1 - P(A)) x (1 - P(B)). It equals 1 - P(A or B), the complement of at least one event happening.
Is my data uploaded anywhere?
No — this calculator runs entirely in your browser; nothing is uploaded.
Is it free?
Yes, completely free with no sign-up and no limits.
People also ask
How do you calculate the probability of two events both happening?
For independent events you multiply their individual probabilities: P(A and B) = P(A) x P(B). For example, two independent events with probabilities 0.5 and 0.4 give 0.5 x 0.4 = 0.2, or a 20 percent chance both occur.
What is the difference between P(A or B) and P(A and B)?
P(A and B) is the chance both events happen at the same time, while P(A or B) is the chance at least one of them happens. For independent events, P(A or B) = P(A) + P(B) - P(A and B), and it is always greater than or equal to either single probability.
How do you convert a probability into odds?
Write the probability as favorable to unfavorable outcomes and reduce the ratio. A probability of 13/52 means 13 favorable and 39 unfavorable outcomes, which reduces to odds of 1 : 3 in favor (one chance for, three against).
What does the complement of an event mean?
The complement is the probability that the event does not happen, equal to 1 minus the event's probability. If an event has probability 0.25, its complement is 0.75, since the two must add up to 1.
Can this calculator handle dependent events?
No. The two-event mode assumes independence and multiplies the two probabilities. For dependent events, where one outcome changes the odds of the other, you would need conditional probability, P(B given A), which this tool does not compute.
How do you turn a probability into a percentage?
Multiply the decimal probability by 100. A probability of 0.2 is 20 percent and 0.25 is 25 percent; the calculator shows this percent automatically in single-event mode.
What is the probability of drawing a specific suit from a deck of cards?
A standard deck has 52 cards with 13 of each suit, so the probability of drawing a given suit is 13/52 = 0.25, or 25 percent. You can reproduce this in single-event mode by entering 13 favorable and 52 total outcomes.
What is the probability of rolling 1, 2, 3, 4, 5, 6 with six dice?
The chance that six dice show each of 1 through 6 exactly once, in any order, is 6! / 6^6 = 720 / 46,656 ≈ 0.0154, or about 1.5% (roughly 1 in 65). If you require a specific order, such as the first die showing 1 and the last showing 6, only one of the 46,656 outcomes works, so the probability is 1 / 46,656 ≈ 0.0000214. Each die is independent, which is why the total outcome count is 6 multiplied by itself six times.
What are the formulas of probability?
The core formulas are: P(event) = favorable outcomes / total outcomes; the complement rule P(not A) = 1 − P(A); the multiplication rule for independent events P(A and B) = P(A) × P(B); and the addition rule P(A or B) = P(A) + P(B) − P(A and B). For dependent events the multiplication rule becomes P(A and B) = P(A) × P(B given A). This calculator applies the first four using the values you enter.
What is the easiest way to solve probability?
Count the outcomes you want and divide by the total number of equally likely outcomes, which is the single-event mode on this page (13 hearts out of 52 cards = 0.25). When the question is whether at least one thing happens, it is usually easier to find the chance that nothing happens and subtract it from 1. For small problems, write out or sketch the outcomes before reaching for a formula, since most errors come from miscounting rather than arithmetic.
What are the three laws of probability?
The three axioms are: every probability is between 0 and 1; the probability of the whole sample space (something happens) is exactly 1; and for events that cannot happen together, P(A or B) = P(A) + P(B). Some textbooks instead call the addition rule, the multiplication rule, and the complement rule the three laws. Every other probability formula, including the ones on this page, follows from these.
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Sources & references
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