Probability Calculator
Solve basic, compound, and conditional probability problems — step-by-step for FBISE, CBSE, IGCSE, O Levels, A Levels & IB.
Select Problem Type
Select a probability type and enter values to see results.
Key Probability Rules
Independent vs Dependent Events
Two events are independent if the occurrence of one has no effect on the probability of the other. For example, flipping a coin twice — the result of the first flip does not affect the second. For independent events, P(A ∩ B) = P(A) × P(B).
Events are dependent when one event affects the probability of the other — for example, drawing cards without replacement. In this case, P(A ∩ B) = P(A) × P(B|A), where P(B|A) is the conditional probability of B given that A has already occurred.
Mutually Exclusive Events
Events are mutually exclusive (or disjoint) if they cannot both occur at the same time. For example, rolling a 3 and rolling a 5 on a single die are mutually exclusive. When events are mutually exclusive, P(A ∩ B) = 0, which simplifies the addition rule to P(A ∪ B) = P(A) + P(B).
Note that mutually exclusive events are never independent (unless at least one has probability 0), because if A occurs, B definitely cannot — so knowing A occurred changes the probability of B.