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Online Probability Calculator
Calculate simple and combined probabilities of events using our easy-to-use online probability calculator. Ideal for statistics, risk assessment, and decision-making.
| 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?
This probability calculator allows you to compute the likelihood of events occurring based on fundamental probability rules. It supports calculations for basic probability, complements, addition, and multiplication of events, making it useful for both simple and combined probability computations.
How to Use This Tool?
- Enter the probability values for events A and B, ensuring they are between 0 and 1.
- Specify whether the events are independent or mutually exclusive, if applicable.
- Select the type of calculation to perform: basic probability, complement, addition, or multiplication.
- Click the calculate button to view the resulting probability value.
- Use the output to analyze or make decisions based on the computed likelihood.
Key Features
- Supports basic probability calculation using favorable and total outcomes.
- Calculates complements of events using the complement rule.
- Computes unions of events using both mutually exclusive and general addition rules.
- Determines joint probabilities for independent events via the multiplication rule.
- Handles variables representing events and their probabilities clearly.
- Uses floating-point arithmetic to ensure precise probability results.
- Browser-based and easy to use without requiring any installation.
Examples
- If event A has a probability of 0.4 and event B has a probability of 0.3, and they are independent, then P(A ∩ B) = 0.4 × 0.3 = 0.12. The probability of either event A or B occurring is P(A ∪ B) = 0.4 + 0.3 − 0.12 = 0.58.
- Using the complement rule, if an event A has P(A) = 0.7, then the probability of A not occurring is P(A') = 1 − 0.7 = 0.3.
- For mutually exclusive events A and B where P(A) = 0.2 and P(B) = 0.5, the probability of A or B occurring is P(A ∪ B) = 0.2 + 0.5 = 0.7.
Common Use Cases
- Evaluating risk levels in various scenarios by calculating probabilities of different outcomes.
- Solving statistics problems involving independent or mutually exclusive events.
- Analyzing games of chance by determining the likelihood of winning combinations.
- Supporting decision-making processes with reliable probability estimates.
- Teaching and learning fundamental concepts in probability and statistics.
Tips & Best Practices
- Always input probability values between 0 and 1 for valid calculations.
- Confirm event independence or exclusivity assumptions before applying relevant formulas.
- Use precise decimal values to improve accuracy in floating-point computations.
- Double-check calculations with multiple rules when applicable to ensure correctness.
- Interpret probability results in context to inform meaningful decisions.
Limitations
- Requires valid input probabilities strictly between 0 and 1 inclusive.
- Results depend on correct assumptions about event independence or exclusivity.
- Cannot handle conditional probabilities or more complex probability distributions.
- Intended for basic and combined probabilities only, not advanced statistical modeling.
Frequently Asked Questions
- Can this calculator handle dependent events?
- No, the calculator assumes independence or mutually exclusive events as specified; dependent events require different calculations not covered here.
- What should I do if my input is outside the valid range?
- Ensure all probability inputs are between 0 and 1. Values outside this range are not valid and will affect the accuracy of the results.
- How is floating-point arithmetic useful in these calculations?
- It allows the calculator to perform precise numerical computations, producing accurate probability values even with decimal inputs.
Key Terminology
- P(A)
- The probability that event A will occur.
- P(B)
- The probability that event B will occur.
- P(A ∩ B)
- The probability that both events A and B occur together.
- P(A ∪ B)
- The probability that event A or B or both occur.
- Complement Rule
- The rule used to find the probability that event A does not occur: P(A') = 1 − P(A).
- Multiplication Rule
- For independent events, the probability that both events occur is the product of their probabilities.
- Addition Rule
- Calculates the probability of either event A or event B occurring, adjusting for overlap if necessary.