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Online Probability Calculator
Probability Calculator finds the probability of two events, solves for unknown probabilities, handles series of independent events, and computes normal distribution areas.
| Result | ||
|---|---|---|
| Probability of A NOT occuring: P(A') | 0.5 | |
| Probability of B NOT occuring: P(B') | 0.6 | |
| Probability of A and B both occuring: P(A∩B) | 0.2 | |
| Probability that A or B or both occur: P(A∪B) | 0.7 | |
| Probability that A or B occurs but NOT both: P(AΔB) = P(A) + P(B) - 2P(A∩B) | 0.5 | |
| Probability of neither A nor B occuring: P((A∪B)') = 1 - P(A∪B) | 0.3 | |
| Probability of A occuring but NOT B: | 0.3 | |
| Probability of B occuring but NOT A: (1 - P(A)) × P(B) | 0.2 | |
Probability
Probability of A: P(A) = 0.5
Probability of B: P(B) = 0.4
Probability of A NOT occuring: P(A') = 0.5
Probability of B NOT occuring: P(B') = 1 - P(B) = 0.6
Probability of A and B both occuring: P(A∩B) = P(A) × P(B) = 0.2
Probability of A and B both occuring: P(A∩B) = P(A) × P(B) = 0.7
Probability that A or B occurs but NOT both: P(AΔB) = P(A) + P(B) - 2P(A∩B) = 0.5
Probability of neither A nor B occuring: P((A∪B)') = 0.3
Probability of A occuring but NOT B: P(A) × (1 - P(B)) = 0.3
Probability of B occuring but NOT A: (1 - P(A)) × P(B) = 0.2
Probability
Probability of A occuring 5 time(s) = 0.65 = 0.07776
Probability of A NOT occuring = (1-0.6)5 = 0.01024
Probability of A occuring = 1-(1-0.6)5 = 0.98976
Probability of B occuring 3 time(s) = 0.33 = 0.027
Probability of B NOT occuring = (1-0.3)3 = 0.343
Probability of B occuring = 1-(1-0.3)3 = 0.657
Probability of A occuring 5 time(s) and B occuring 3 time(s) = 0.65 ×
0.33 = 0.00209952
Probability of neither A nor B occuring = (1-0.6)5 × (1-0.3)3 =
0.00351232
Probability of both A and B occuring = (1-(1-0.6)5) × (1-(1-0.3)3) =
0.65027232
Probability of A occuring 5 times but not B = 0.65 × (1-0.3)3 =
0.02667168
Probability of B occuring 3 times but not A = (1-0.6)5 × 0.33 =
2.7648e-4
Probability of A occuring but not B = (1-(1-0.6)5) × (1-0.3)3 =
0.33948768
Probability of B occuring but not A = (1-0.6)5 × (1-(1-0.3)3) =
0.00672768
Probability
The probability between -1 and 1 is 0.68268
The probability outside of -1 and 1 is 0.31732
The probability of -1 or less (≤-1) is 0.15866
The probability of 1 or more (≥1) is 0.15866
| CONFIDENCE INTERVALS TABLE | ||
|---|---|---|
| CONFIDENCE | RANGE | N |
| 0.6828 | -1.00000 – 1.00000 | 1 |
| 0.8 | -1.28155 – 1.28155 | 1.281551565545 |
| 0.9 | -1.64485 – 1.64485 | 1.644853626951 |
| 0.95 | -1.95996 – 1.95996 | 1.959963984540 |
| 0.98 | -2.32635 – 2.32635 | 2.326347874041 |
| 0.99 | -2.57583 – 2.57583 | 2.575829303549 |
| 0.995 | -2.80703 – 2.80703 | 2.807033768344 |
| 0.998 | -3.09023 – 3.09023 | 3.090232306168 |
| 0.999 | -3.29053 – 3.29053 | 3.290526731492 |
| 0.9999 | -3.89059 – 3.89059 | 3.890591886413 |
| 0.99999 | -4.41717 – 4.41717 | 4.417173413469 |
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What Is This Tool?
The Probability Calculator covers four common probability tasks in one place. The two-events mode takes P(A) and P(B) and returns every combined probability — A and B, A or B, exactly one, neither, and so on — illustrated with Venn diagrams. The solver mode works backwards, finding unknown probabilities from two known values. The series mode handles independent events repeated several times, and the normal distribution mode computes areas under a normal curve along with confidence intervals. Pick a mode from the dropdown, enter the values, and the result can be downloaded as a PDF.
How to Use This Tool?
- Choose a mode from the dropdown.
- Enter the probabilities or parameters it asks for.
- Click Calculate to see the results.
- Download a PDF of the result if you'd like.
Key Features
- Calculates all combined probabilities of two events (and, or, exactly one, neither).
- Solves for unknown probabilities from two known values.
- Handles a series of independent repeated events.
- Computes normal distribution probabilities and confidence intervals.
- Illustrates two-event results with Venn diagrams and offers a PDF download.
Examples
- With P(A) = 0.5 and P(B) = 0.4, P(A and B) = 0.2 and P(A or B) = 0.7.
- Knowing P(A∩B) and P(A∪B), the solver finds P(A) and P(B).
- An event with probability 0.6 repeated 5 times has a 0.07776 chance of occurring every time.
- For a standard normal curve, the area between −1 and 1 is about 0.68268.
Common Use Cases
- Working out combined event probabilities.
- Filling in missing probabilities from known ones.
- Estimating outcomes over repeated independent trials.
- Finding areas and confidence intervals under a normal curve.
- Checking probability homework or coursework.
Tips & Best Practices
- Enter probabilities as decimals between 0 and 1.
- For the solver, pick two compatible known events.
- Use whole numbers for repetition counts.
- For the normal distribution, set the mean, standard deviation, and bounds.
- Apply the independence assumption only when events truly don't affect each other.
Limitations
- The two-events and series modes assume the events are independent.
- Normal distribution results rely on a standard z-table approximation.
- The solver needs two compatible inputs, or it can't find a solution.
- Nothing is saved between sessions — only the current result can be exported as a PDF.
Frequently Asked Questions
- What does the two-events mode calculate?
- It returns every combined probability of two events — both occurring, either occurring, exactly one, and neither.
- What does 'independent' mean here?
- Independent events are those where one occurring doesn't change the probability of the other.
- How does the solver work?
- It uses algebra to derive the remaining probabilities from the two known values you provide.
- What are the confidence intervals?
- They are ranges around the mean of a normal distribution that contain a given proportion of the data.
Key Terminology
- Probability
- A number between 0 and 1 expressing how likely an event is.
- Independent events
- Events where one occurring doesn't change the probability of the other.
- Union (A∪B)
- The event that A or B (or both) occur.
- Intersection (A∩B)
- The event that both A and B occur.
- Normal distribution
- A symmetric bell-shaped distribution described by its mean and standard deviation.