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Probability Calculator - Calculate Probability Distributions

How Does the Probability Calculator Work?

P(A) = Number of favorable outcomes / Total number of outcomes | P(A or B) = P(A) + P(B) - P(A and B) | P(A and B) = P(A) × P(B) for independent events

Enter your data in the fields provided and get an immediate, accurate result you can rely on for everyday use.

  1. 1

    Step 1

    Identify the type of probability problem (simple, compound, or conditional)

  2. 2

    Step 2

    Enter the number of favorable outcomes and total outcomes

  3. 3

    Step 3

    Select the probability operation (AND, OR, NOT)

  4. 4

    Step 4

    Click calculate to get the probability result

  5. 5

    Step 5

    Review the step-by-step solution and interpretation

Use Cases

Calculating winning odds in lottery and gambling

Risk assessment in insurance and finance

Quality control and defect probability in manufacturing

Medical diagnosis probability calculations

Sports betting odds analysis

Weather forecasting probability models

Tips

  • 1

    Probability values always range from 0 (impossible) to 1 (certain)

  • 2

    The sum of all probabilities in a sample space equals 1

  • 3

    Use the multiplication rule for AND probabilities of independent events

  • 4

    Use the addition rule for OR probabilities, subtracting overlap for non-mutually exclusive events

  • 5

    Conditional probability P(A|B) = P(A and B) / P(B)

Common Mistakes

  • Confusing independent and dependent events when multiplying probabilities

  • Forgetting to subtract P(A and B) when using the addition rule for non-mutually exclusive events

  • Assuming events are independent without verification

  • Confusing probability with odds - they are different concepts

  • Not considering all possible outcomes in the sample space

FAQs

What is the difference between probability and odds?

Probability is the ratio of favorable outcomes to total outcomes (e.g., 1/6 for rolling a specific number on a die). Odds compare favorable to unfavorable outcomes (e.g., 1:5 for the same scenario). To convert odds to probability: P = odds / (1 + odds).

How do I calculate the probability of multiple events occurring?

For independent events both occurring (AND), multiply their probabilities: P(A and B) = P(A) × P(B). For either event occurring (OR), add probabilities and subtract overlap: P(A or B) = P(A) + P(B) - P(A and B).

What is conditional probability?

Conditional probability P(A|B) is the probability of event A occurring given that event B has already occurred. It's calculated as P(A|B) = P(A and B) / P(B). This is fundamental in Bayesian statistics and decision-making under uncertainty.

Why is my probability greater than 1?

A probability greater than 1 indicates an error. Check that favorable outcomes don't exceed total outcomes, and when using the addition rule, ensure you're subtracting the intersection P(A and B) for non-mutually exclusive events.

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