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 - मुफ़्त ऑनलाइन कैलकुलेटर
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.
- सूत्र पेज पर दिखता है
- आपके ब्राउज़र में चलता है
- आपकी जानकारी निजी रहती है
Probabilities can be entered as decimals (0.5) or fractions (1/2).
P(event) = 1 / 6
0.166667 (16.6667%)
Equally likely outcomes assumed.
कुछ सामग्री अब भी अंग्रेज़ी में दिखती है।
Probability Calculator को समझें
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.
Probability Calculator को 5 चरणों में इस्तेमाल करें
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.
Probability Calculator कैसे काम करता है
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)
Probability Calculator जवाब कैसे निकालता है
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.
हल किए उदाहरण
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.
Probability Calculator कब इस्तेमाल करें
- 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.
आम गलतियाँ और सावधानियाँ
- 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.
इस टूल का ज़्यादा फ़ायदा उठाएँ
- 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.
Probability Calculator के बारे में सवाल
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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