Single, Multiple, Joint & Conditional Probability Calculator

No.of Possible Outcomes (n)
No.of events occured n(A)
No.of events occured n(B)
P(A)  =  0.57
P(A')  =  0.43
P(B)  =  0.43
P(B')  =  0.57
P(A n B)  =  0.24
P(A U B)  =  0.76
P(A | B)  =  0.57

Probability Calculation - work with steps

Input Data :
Number of possible outcomes - n = 14
Number of events occured - n(A) = 8
Number of events occured - n(B) = 6

Objective :
Find what is P(A) , P(a), P(B), P(b), P(Aub), p(Anb) & P(A|B)

Formula :
P(A) = No.of events occured- n(A)No.of Possible Outcomes- n
P(A) = 1 - P(A)
P(B) = No.of events occured- n(B)No.of Possible Outcomes- n
P(B) = 1 - P(B)
P(A∩B) = P(A) x P(B)
P(AUB) = P(A) + P(B) - P(A∩B)
P(A|B) = P(A∩B)P(B)

Solution :
P(A) = 814
P(A) = 0.57

P(A') = 1 - P(A)
P(A') = 0.43

P(B) = 614
P(B) = 0.43

P(B') = 1 - P(A)
P(B') = 0.57

P(A∩B) = 0.57 x 0.43
P(A∩B) = 0.25

P(AUB) = 0.57 + 0.43 - 0.25
P(AUB) = 1 - 0.25
P(AUB) = 0.75

P(A|B) = 0.250.43
P(A|B) = 0.58

Probability Calculation

Probability Calculator is an online tool for risk analysis specially programmed to find out the probability for single event and multiple events. In this mathematical definition of probability can extend to infinite sample spaces, and even uncountable sample spaces, using the concept of a measure.


Probability is a way of expressing knowledge or belief that an event will occur or has occurred. Probability theory is applied in everyday life in risk assessment and in trade on commodity markets.

Probability and Formulas

Probability of Single Event

The probability of single event A is written as P(A), p(A) or Pr(A).

Single Event Complement Probability

The opposite or complement of an event A is the event that is, the event of A not occurring; its probability is given by the formula.
P(not A) = 1 - P(A)

Joint Probability of Multiple Events

If both events A and B occur on a single performance of an experiment, this is called the intersection or joint probability of A and B, denoted as P(A n B). If two events, A and B are independent then the joint probability can be derived from the formula.
P(A n B) = P(A) P(B)

Probability of Mutually Exclusive Events

If either event A or event B or both events occur on a single performance of an experiment this is called the union of the events A and B denoted as P(A U B). If two events are mutually exclusive then the probability of either occurring can be derived from the formula.
P(A U B) = P(A) + P(B)

If the events are not mutually exclusive then
P(A U B) = P(A) + P(B) - P(A n B)

Conditional Probability

Conditional probability is the probability of some event A, given the occurrence of some other event B. Conditional probability is written P(A|B), and is read the probability of A, given B. It can be derived from the below formula.
P(A | B) = P(A n B)/P(B)

If P(B) = 0 then P(A | B) is undefined. Note that in this case A and B are independent.

The collection of tools employs the study of methods and procedures used for gathering, organizing, and analyzing data to understand theory of Probability and Statistics. The set of ideas which is intended to offer the way for making scientific implication from such resulting summarized data. In many applications it is necessary to calculate the probability of single event, multiple event, joint probability, conditional probability and etc. to make your complicated calculations easy, this online probability calculator can help you to find out the event occurrences.