Probability Calculator

1. Single Event. Enter the number of favorable outcomes and total possible outcomes. P(A) = favorable / total. Rolling a 3 on a die: 1 favorable out of 6 total = 0.1667 (16.67%). The result also shows P(not A), odds in favor, and odds against.
2. Two Events. Enter P(A) and P(B) as decimals between 0 and 1. Check the "independent" box if the events do not affect each other (like two coin flips). Results include P(A and B), P(A or B), P(A given B), and P(neither A nor B).
3. Combination C(n,r). Enter n (total items) and r (items chosen). Order does not matter. Example: choosing 3 people from a group of 10 gives C(10,3) = 120 possible groups.
4. Permutation P(n,r). Enter n and r when order matters. Arranging 3 people from 10 in specific positions gives P(10,3) = 720 arrangements.

Single Event:         P(A) = favorable outcomes / total outcomes

Complement:           P(not A) = 1 - P(A)

Independent AND:      P(A and B) = P(A) x P(B)
Dependent AND:        P(A and B) = P(A) x P(B|A)

OR (any events):      P(A or B) = P(A) + P(B) - P(A and B)
Mutually exclusive:   P(A or B) = P(A) + P(B)

Combination C(n,r):   n! / (r! x (n-r)!)
Permutation P(n,r):   n! / (n-r)!

Examples with a standard deck of 52 cards: