Probability Calculator

Calculate probabilities for single events, compound events, and complements with detailed explanations.

Probability Calculations

Select mode and enter probabilities

Calculation Mode

Favorable Outcomes

Total Outcomes

P(A)

P(B)

Event Relationship

P(B|A) — Probability of B given A

P(A)

P(B)

P(A ∩ B) — Both events occurring

P(A)

Probability

Select a mode and enter values above, then tap Calculate.

Step-by-step Solution

Probability Formulas

Basic:
P(A) = Favorable / Total

AND (indep):
P(A∩B) = P(A) × P(B)

AND (dep):
P(A∩B) = P(A) × P(B|A)

OR:
P(A∪B) = P(A) + P(B) − P(A∩B)

Complement:
P(A') = 1 − P(A)

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Key Concepts

Mutually Exclusive: Two events that cannot occur simultaneously. If A and B are mutually exclusive, P(A∩B) = 0.

Independent Events: The occurrence of one event does not affect the probability of the other. P(B|A) = P(B).

Dependent Events: The outcome of one event affects the probability of another. Use conditional probability P(B|A).

Complement Rule: The probability that an event does NOT occur is 1 minus the probability it does occur.