Two dice rolled - probability that the sum is 7?
Total outcomes: 6×6 = 36. Favorable (sum = 7): (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6. P = 6/36 = 1/6 ≈ 0.167. Sum of 7 is the most likely sum from two dice.
Probability Calculator - Calculatrice en ligne gratuite
Compute single-event probability, joint (AND), union (OR), conditional and complement probabilities - all in one tool. Modes cover both independent events and mutually exclusive events. Useful for class 11/12 board exam practice, JEE prep, dice and coin problems, and basic risk analysis.
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Probabilities can be entered as decimals (0.5) or fractions (1/2).
P(event) = 1 / 6
0.166667 (16.6667%)
Equally likely outcomes assumed.
Une partie du contenu est encore affichée en anglais.
Comprendre : Probability Calculator
Probability theory underlies modern statistics, machine learning, insurance pricing, risk assessment, scientific hypothesis testing, and game-of-chance analysis. It also forms a major part of Class 11-12 mathematics in CBSE/ICSE curricula and is regularly tested in JEE Main, JEE Advanced, and NEET. Understanding probability - and being able to compute joint, union, conditional and complement probabilities reliably - is a foundational quantitative skill.
This calculator handles the five most-asked probability questions: single-event probability (favorable outcomes / total outcomes), joint probability of two independent events (P(A AND B) = P(A) × P(B)), union probability (P(A OR B), supporting both mutually exclusive and general cases), conditional probability (P(A|B) = P(A AND B) / P(B)), and complement probability (P(A') = 1 − P(A)). Toggle between modes for different problem types, and use the formula display to verify and learn.
Utiliser Probability Calculator en 5 étapes
Pick the mode that matches your problem.
Enter the probabilities in decimal (0.5) or fraction-style (1/2) - both are accepted.
For multi-event modes, enter both event probabilities.
Read the result, and the formula used to compute it.
Switch modes any time - your inputs are preserved when possible.
Comment fonctionne Probability Calculator
Probability is a number between 0 (impossible) and 1 (certain). Single-event probability divides favorable outcomes by total outcomes. For two independent events A and B, P(A AND B) = P(A) × P(B). For mutually exclusive events, P(A OR B) = P(A) + P(B). For general (overlapping) events, P(A OR B) = P(A) + P(B) − P(A AND B). Conditional probability P(A | B) = P(A AND B) / P(B). The complement is just 1 − P(A).
Formula
P(A AND B) = P(A) × P(B) P(A OR B) = P(A) + P(B) − P(A AND B)
- P(A)Probability of event A
- ANDBoth events occur (independent: multiply)
- OREither event occurs (mutually exclusive: add)
- P(A|B)Conditional - A given B occurred
- P(A')Complement - event A does not occur = 1 − P(A)
Comment Probability Calculator obtient son résultat
Single-event probability: P(A) = number of favorable outcomes / total number of outcomes. Example: rolling a 6 on a fair die - 1 favorable / 6 total = 1/6 ≈ 0.167. Drawing an Ace from a 52-card deck - 4 favorable / 52 total = 1/13 ≈ 0.077. The result is always between 0 and 1; multiply by 100 to express as a percentage.
Joint probability of two events: if A and B are independent (one doesn't affect the other), P(A AND B) = P(A) × P(B). Two coin flips: P(both heads) = 0.5 × 0.5 = 0.25. If A and B are dependent, use conditional probability: P(A AND B) = P(A) × P(B|A). Drawing two cards without replacement: P(both Aces) = (4/52) × (3/51) = 1/221.
Union probability: if A and B are mutually exclusive (can't occur together), P(A OR B) = P(A) + P(B). Rolling a die - P(2 or 5) = 1/6 + 1/6 = 2/6. If they can overlap, subtract the joint to avoid double-counting: P(A OR B) = P(A) + P(B) − P(A AND B). Drawing a card - P(Ace or Spade) = 4/52 + 13/52 − 1/52 = 16/52 (the Ace of Spades is counted once, not twice).
Complement and conditional: P(A') = 1 − P(A) is invaluable for 'at least one' problems. P(at least 1 head in 3 flips) = 1 − P(all tails) = 1 − (1/2)³ = 7/8. Conditional probability P(A|B) = P(A AND B) / P(B) is the probability of A given that B already occurred. Used in medical testing, Bayesian inference, machine learning.
Exemples résolus
At least 1 head in 4 coin flips
P(no heads in 4 flips) = (1/2)^4 = 1/16. P(at least 1 head) = 1 − 1/16 = 15/16 = 93.75%. Complement makes this easy.
Drawing two cards without replacement, both Kings
First King: 4/52. Second King given first was King: 3/51. P(both) = (4/52) × (3/51) = 12/2652 = 1/221 ≈ 0.0045. Conditional probability handles the dependence cleanly.
Quand utiliser Probability Calculator
- Class 11-12 mathematics probability chapter - homework and exam prep.
- JEE Main and JEE Advanced probability questions (frequently tested).
- NEET probability problems for medical entrance preparation.
- Card game probability analysis (poker, rummy, bridge).
- Dice game probability - board games, gambling theory.
- Insurance and risk analysis where compound event probabilities matter.
- Quality control where defect probabilities across multiple production stages need to be combined.
Erreurs et pièges courants
- Treating dependent events as independent. P(both Aces in 2 draws) ≠ (4/52)² when drawing without replacement.
- Forgetting to subtract overlap in OR probability. P(A or B) = P(A) + P(B) only if A and B are mutually exclusive.
- Confusing 'at least one' with 'exactly one'. They're different probabilities.
- Computing P > 1. Always sanity-check; any P > 1 indicates a mistake (often double-counting overlap).
- Forgetting that conditional probability changes the sample space - P(B|A) is computed within the world where A occurred.
Tirez le meilleur de cet outil
- Use the complement formula for 'at least one' problems - much easier than direct computation.
- Draw a tree diagram for compound events with multiple steps and dependence.
- Check independence carefully - dice and coins are independent, drawing without replacement isn't.
- When in doubt, use the general OR formula with the subtraction term. It always works (subtracts to zero if mutually exclusive).
- Pair this calculator with the permutation-combination, sample-size and z-score calculators on this site for related statistical analyses.
Questions sur Probability Calculator
What is probability?
A measure of how likely an event is, between 0 and 1 (or 0% and 100%). Throwing a fair die: P(getting a 6) = 1/6 ≈ 0.1667. P(any number from 1 to 6) = 1 (certain).
What is the difference between independent and mutually exclusive events?
Independent: one event doesn't affect the other (rolling two dice). Mutually exclusive: events can't happen together (rolling a die: you can't get both a 2 and a 5 in the same throw).
How do I compute P(A AND B)?
If A and B are independent: P(A) × P(B). If they're not independent, you need conditional probability: P(A AND B) = P(A) × P(B|A). Use the AND mode for the independent case.
How do I compute P(A OR B)?
If A and B are mutually exclusive: P(A) + P(B). If they can overlap: P(A) + P(B) − P(A AND B). The OR mode supports both - toggle the "mutually exclusive" checkbox.
What is conditional probability?
P(A | B) is the probability of A given that B has happened. Formula: P(A AND B) / P(B). Example: drawing two cards without replacement - P(2nd Ace | 1st Ace) = 3/51, since one ace is gone.
What is the complement of an event?
The complement of A, denoted A' or Aᶜ, is "A doesn't happen". P(A') = 1 − P(A). Useful when computing "at least one" type problems is easier as 1 − P(none).
Can probability be greater than 1?
No. If your calculation gives a probability > 1, you've likely double-counted overlap - use the OR formula with the subtraction term, or check whether your events are really mutually exclusive.
What's the probability of getting at least one head in 3 coin flips?
Easier as the complement: P(no heads) = (1/2)³ = 1/8. So P(at least one head) = 1 − 1/8 = 7/8 = 87.5%.
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If you're a student, double-check your work without paying for a graphing calculator. If you're a professional, use these tools as a sanity check on spreadsheet formulas. Every result is shown alongside its formula and inputs, so the math is always auditable.
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