Probability Formulas

The Single Event Probability Calculator uses the following formulas:

P(E) = n(E) / n(T) = (number of outcomes in the event) / (total number of possible outcomes)

P(E') = P(not E) = 1 - P(E)

Where,

P(E) is the probability that the event will occur,

P(E') is the probability that the event will not occur,

n(E) is the number of outcomes in the event E,

n(T) is the total number of possible outcomes.

Probability Formulas

The Multiple Event Probability Calculator uses the following formulas:

P(A) = n(A) / n(T)

P(B) = n(B) / n(T)

Single Event Complement Probability

P(A') = P(not A) = 1 - P(A)

P(B') = P(not B) = 1 - P(B)

Joint Probability of Multiple Events

P(A ∩ B) = P(A) × P(B)

Probability of Mutually Exclusive Events

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Conditional Probability

P(A | B) = P(A ∩ B) / P(B)

P(B | A) = P(A ∩ B) / P(A)

Where,

P(A) is the probability that event A occurs,

P(A') is the probability that event A does not occur,

P(B) is the probability that event B occurs,

P(B') is the probability that event B does not occur,

P(A ∩ B) is the probability that events A and B both occur,

P(A ∪ B) is the probability that events A or B occur,

P(A | B) is the probability that event A occurs, given that event B has occurred,

n(A) is number of outcomes in the event A,

n(B) is number of outcomes in the event B,

n(T) is total number of possible outcomes.