Probability Calculator
Probability measures likelihood of events from 0 (impossible) to 1 (certain), expressed as decimal, fraction, or percentage. Formula: P(event) = favorable outcomes / total outcomes. For dice: P(rolling 4) = 1/6 ≈ 16.67%. Independent events multiply: P(two heads) = 0.5 × 0.5 = 0.25. Mutually exclusive events add: P(rolling 1 or 6) = 1/6 + 1/6 = 1/3. Conditional probability: P(A|B) = P(A and B) / P(B). Use for risk assessment, statistics, gambling odds.
Calculate probabilities for single and two events, permutations (nPr), combinations (nCr), factorials, and Bayes' theorem. Toggle independent vs dependent events, see conditional probabilities P(A|B), and visualize with a Venn diagram. Step-by-step solutions with formulas.
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Single Event Probability
How to Use
- Enter your value in the input field
- Click the Calculate/Convert button
- Copy the result to your clipboard
Frequently Asked Questions
- How do I calculate the probability of two independent events both happening?
- For independent events, multiply their individual probabilities: P(A and B) = P(A) × P(B). For example, if P(A) = 0.5 and P(B) = 0.3, then P(A and B) = 0.5 × 0.3 = 0.15 or 15%. Events are independent when one does not affect the other, like two separate coin flips.
- What is the difference between permutations and combinations?
- Permutations (nPr) count arrangements where order matters: P(n,r) = n!/(n−r)!. Combinations (nCr) count selections where order does not matter: C(n,r) = n!/(r!(n−r)!). Choosing 3 people from 10 for president/VP/treasurer is a permutation (720). Choosing 3 from 10 for a committee is a combination (120).
- What is Bayes' theorem and when do I use it?
- Bayes' theorem calculates updated probability after new evidence: P(A|B) = P(B|A) × P(A) / P(B). Use it when you know the likelihood of evidence given a hypothesis and want the probability of the hypothesis given the evidence. Classic example: medical testing — given a positive test result, what is the actual probability of having the disease?
- What is conditional probability P(A|B)?
- Conditional probability P(A|B) is the probability of event A occurring given that event B has already occurred. Formula: P(A|B) = P(A and B) / P(B). For example, the probability of drawing a king given that a face card was drawn is P(King|Face) = (4/52) / (12/52) = 1/3.
- What is the complement rule in probability?
- The complement rule states P(not A) = 1 − P(A). If the probability of rain is 0.3, the probability of no rain is 0.7. This is useful when calculating "at least one" probabilities: P(at least one) = 1 − P(none). For example, probability of at least one head in 3 coin flips = 1 − (0.5)³ = 0.875.
- How do I calculate P(A or B)?
- Use the addition rule: P(A or B) = P(A) + P(B) − P(A and B). You subtract P(A and B) to avoid double-counting outcomes in both events. For mutually exclusive events (cannot both happen), P(A and B) = 0, so P(A or B) = P(A) + P(B).