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Statistics CalculatorStatistics Calculator

Probability Calculator

Find the probability of two events happening together or separately. Enter P(A) and P(B) to get P(A and B), P(A or B), the complements, and the conditional probability.

Tested against reference valuesLast reviewed August 2026
P(A and B)
0.1500
P(A or B)
0.6500
P(not A)
0.5000
P(not B)
0.7000
P(A | B)
0.5000

How to use this calculator

  1. Enter the probability of each event as a decimal between 0 and 1.
  2. Choose whether the events are independent or mutually exclusive.
  3. Read the combined and complementary probabilities.

The probability rules

For independent events, whether one happens does not change the other:

P(AB)=P(A)P(B),P(AB)=P(A)+P(B)P(A)P(B)P(A \cap B)=P(A)\,P(B),\quad P(A \cup B)=P(A)+P(B)-P(A)P(B)

For mutually exclusive events, both cannot happen at once:

P(AB)=0,P(AB)=P(A)+P(B)P(A \cap B)=0,\quad P(A \cup B)=P(A)+P(B)

The complement of an event is P(not A) = 1 − P(A), and the conditional probability is P(A | B) = P(A ∩ B) / P(B).

Independent vs. mutually exclusive

Independent and mutually exclusive are not the same. Independent events can both occur; mutually exclusive events cannot. In fact, two events with non-zero probability that are mutually exclusive are never independent.

Frequently asked questions

What is the difference between independent and mutually exclusive events?

Independent events do not affect each other and can both occur. Mutually exclusive events cannot occur at the same time, so their joint probability is zero. Two events with positive probability cannot be both independent and mutually exclusive.

How do I find P(A and B)?

For independent events, multiply the probabilities: P(A and B) = P(A) × P(B). For mutually exclusive events, P(A and B) = 0 because they cannot both happen.

What is conditional probability?

Conditional probability P(A | B) is the probability of A given that B has occurred. It equals P(A and B) divided by P(B).

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