Free Probability Calculator Online
This free online probability calculator computes single and combined event probabilities — including union, intersection, complement, and conditional probability.
Event Probabilities
Union P(A ∪ B)
Enter probabilities above
How the Probability Calculator Works
The probability calculator takes one or two event probabilities and computes several useful values. Enter your probabilities as decimals (0 to 1) or percentages (0% to 100%) and select whether the events are independent or dependent.
For a single event with probability P(A) = 0.6, the complement is P(A′) = 1 − 0.6 = 0.4. That means a 60% chance of occurrence and a 40% chance it does not happen. The probability calculator shows both values instantly.
For two events, the probability calculator computes the intersection (both events), union (either event), and conditional probability. These cover most real-world probability questions from coin flips to risk assessment.
Key Probability Formulas
Complement
P(A′) = 1 − P(A)
Intersection (Independent)
P(A ∩ B) = P(A) × P(B)
Union
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
Conditional
P(A | B) = P(A ∩ B) / P(B)
Practical Probability Examples
Coin Flips
Each coin flip has P = 0.5. The probability of three heads in a row is 0.5 × 0.5 × 0.5 = 0.125 (12.5%). Use the probability calculator with P(A) = P(B) = 0.5 for two-flip scenarios, then chain the results for more flips.
Dice Rolls
Rolling a specific number on a six-sided die has P = 1/6 ≈ 0.1667. The probability of NOT rolling a 6 is the complement: 1 − 0.1667 = 0.8333. Use the probability calculator to explore combined die outcomes quickly.
Card Drawing
Drawing an ace from a standard deck has P = 4/52 ≈ 0.0769. Drawing a heart has P = 13/52 = 0.25. The probability of drawing the ace of hearts is the intersection: 1/52 ≈ 0.0192. The probability calculator handles these joint probabilities.
Tips for Using the Probability Calculator
Independent vs. Dependent
Events are independent if one does not affect the other (coin flips, dice rolls). They are dependent if one changes the odds of the other (drawing cards without replacement). The probability calculator assumes independence by default.
Enter as Decimal or %
You can enter probability as a decimal between 0 and 1, or as a percentage. The probability calculator accepts both formats and converts automatically for your convenience.
Check the Complement
Sometimes it is easier to calculate the probability something does NOT happen, then subtract from 1. The probability calculator shows complements so you always have both perspectives.
Validate Your Input
Probabilities must be between 0 and 1 (or 0% and 100%). If you get an error, double-check that your values are in range. The probability calculator validates inputs automatically.
Frequently Asked Questions
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