Probability Calculator
Compute Gaussian distribution tails and independent event intersections. Map Z-scores to CDF values using precision floating-point logic. Resolve P(A∩B).
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About Probability Calculator
Use this probability calculator for independent two-event probabilities and basic normal distribution interval estimates.
How to Use
Choose a probability mode and enter the required values.
- Select two events or normal distribution.
- Enter probabilities or distribution parameters.
- Review the calculated probability values.
Examples
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Two independent events
P(A): 0.5 P(B): 0.4 P(not A): 0.5 P(not B): 0.6 P(A and B): 0.2 P(A or B): 0.7 P(exactly one): 0.5 P(neither): 0.3
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Standard normal interval
Distribution: Normal Mean: 0 Standard deviation: 1 Lower value: -1 Upper value: 1 Left-tail probability: 0.158655 Probability between -1 and 1: 0.682689 Right-tail probability: 0.158655
Real-World Usage Scenarios
- System Redundancy - Risk Assessment - Calculate the probability of total system failure by treating two independent backup components as independent events. If both fail simultaneously, the system goes down.
- Industrial Quality Control - Tolerance Testing - Use the normal distribution mode to determine the percentage of manufactured parts that fall outside acceptable tolerance limits based on mean and standard deviation.
- Marketing Conversion Funnels - Multi-Step Logic - Estimate the likelihood of a user completing two unrelated actions, such as clicking a specific banner and signing up for a newsletter, to model cross-channel conversion.
- Finance - Portfolio Volatility - Assess the probability of an asset's price staying within a specific range over a period, assuming returns follow a normal distribution pattern.
Frequently Asked Questions
What is the difference between P(A and B) and P(A or B)?
P(A and B) represents the intersection where both events occur, while P(A or B) represents the union where at least one of the two events occurs.
How does the calculator handle the independence of events?
The tool assumes events A and B are independent. This means the occurrence of one does not affect the probability of the other, allowing the use of the multiplication rule.
Why use the Normal Distribution mode instead of Two Events?
The Normal Distribution mode is for continuous data (like height or test scores) to find probabilities within a range, whereas Two Events is for discrete, binary outcomes.
Can I calculate Z-scores with this tool?
Yes. By inputting the mean, standard deviation, and your X values, the tool calculates the area under the curve, which corresponds to Z-score probabilities.
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