Probability Calculator Online Free Tool
Probability Calculator
Probability Calculations
Select a calculation type and enter values to compute probabilities instantly
Probability of Two Independent Events
Calculate union, intersection, and related probabilities
Input Probabilities
Calculated Probabilities
Probability measures how likely an event is to occur, expressed as a value between 0 (impossible) and 1 (certain), or equivalently 0% to 100%. This calculator handles the most common probability problems: single events, compound events (AND/OR), conditional probability, and the complement rule.
Basic Probability Rules
The probability of an event equals the number of favorable outcomes divided by the total number of possible outcomes, assuming all outcomes are equally likely.
P(A) = Favorable Outcomes / Total Outcomes Complement: P(not A) = 1 - P(A) AND (independent): P(A and B) = P(A) × P(B) OR (mutually exclusive): P(A or B) = P(A) + P(B) OR (not mutually exclusive): P(A or B) = P(A) + P(B) - P(A and B)
Example: Probability of rolling a 6 on a fair die = 1/6 ≈ 16.7%.
Conditional Probability
Conditional probability P(A|B) asks: given that B has occurred, what is the probability of A? This is used when events are dependent on each other.
P(A|B) = P(A and B) / P(B)
Example: If 30% of students play sports and 20% play sports and are on honor roll, then given that a student plays sports, P(honor roll | sports) = 0.20 / 0.30 = 66.7%.
Frequently Asked Questions
What is the difference between independent and dependent events?⌄
Independent events do not affect each other's probability. Rolling a die twice: the second roll is independent of the first. Dependent events affect each other. Drawing cards without replacement: removing one card changes the probabilities for subsequent draws.
What is the Law of Large Numbers?⌄
As the number of trials increases, the observed frequency of outcomes approaches the theoretical probability. Flip a fair coin 10 times and you might get 7 heads. Flip it 10,000 times and you will be very close to 50%. This is why probability describes long-run behavior, not any specific sequence of events.
What is the difference between probability and odds?⌄
Probability = favorable outcomes / total outcomes. Odds = favorable outcomes / unfavorable outcomes. For an event with probability 0.25, the odds are 1:3 (1 favorable for every 3 unfavorable). Sports betting and gambling commonly use odds notation rather than probability.
What is a probability distribution?⌄
A probability distribution describes the probability of each possible outcome. For a fair six-sided die, each outcome has probability 1/6 and the distribution is uniform. For complex real-world events, distributions like normal (bell curve), binomial, or Poisson describe how probabilities are spread across outcomes.