Probability Calculator

Calculate probabilities for various scenarios including two events, series of independent events, and normal distributions

Calculate probabilities for various scenarios including two events, series of independent events, and normal distributions.

Probability of Two Events

To find out the union, intersection, and other related probabilities of two independent events.

Please input values between 0 and 1.

Probability Solver for Two Events

Please provide any 2 values below to calculate the rest probabilities of two independent events.

Please input values between 0 and 1.

Probability of a Series of Independent Events

Event
Probability
Repeat Times
Event A
Event B

Probability of a Normal Distribution

Use the calculator below to find the area P shown in the normal distribution, as well as the confidence intervals for a range of confidence levels.

For negative infinite, use -inf
For positive infinite, use inf
μσL_bR_bN(μ, σ²)

About Probability Calculations

Probability is a fundamental concept in mathematics and statistics that measures the likelihood of events occurring.

Key Concepts:

  • Union (A∪B): Probability of A or B or both occurring
  • Intersection (A∩B): Probability of both A and B occurring
  • Complement (A'): Probability of A not occurring
  • Symmetric Difference (AΔB): Probability of A or B but not both

Normal Distribution:

Mean (μ): Center of the distribution
Standard Deviation (σ): Spread of the distribution
68-95-99.7 Rule: Empirical rule for normal distributions
Z-Score: Number of standard deviations from mean

Applications:

  • • Statistical analysis and research
  • • Risk assessment and insurance
  • • Quality control and manufacturing
  • • Financial modeling and investments
  • • Medical research and clinical trials
  • • Machine learning and AI

Important Rules:

  • • Probabilities range from 0 to 1
  • • P(A') = 1 - P(A)
  • • P(A∪B) = P(A) + P(B) - P(A∩B)
  • • For independent events: P(A∩B) = P(A) × P(B)
  • • Total probability of all outcomes = 1