Probability Calculator Online

Probability is the chance that given event will occur. It is expressed as a number between 0 and 1 (where 0 shows false and 1 shows true). The higher the probability of an event, the more certain that the event will occur. In this online probability calculator, calculate the single and multiple event probability based on number of possible outcomes and events occurred. Probabilities in general describes the underlying mechanics and regularities of complex systems.

Single Event Probability

Result



Multiple Event Probability

Result

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Single Event Probability Formula :

Probability of event A that occurs P(A) = n(A) / n(S). Probability of event A that does not occur P(A') = 1 - P(A).

Multiple Event Probability Formula :

Probability of event A that occurs P(A) = n(A) / n(S). Probability of event A that does not occur P(A') = 1 - P(A). Probability of event B that occurs P(B) = n(B) / n(S). Probability of event B that does not occur P(B') = 1 - P(B). Probability that both the events occur P(A ∩ B) = P(A) x P(B). Probability that either of event occurs P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Conditional Probability P(A | B) = P(A ∩ B) / P(B). Where, n(A) - Number of Occurrence in Event A, n(B) - Number of Occurrence in Event B, n(S) - Total Number of Possible Outcomes.

Example

Single Event Probability

Find single event probabilitiy, given n(s) = 20, P(A) = 13

Step 1 : To find P(A)
         P(A) = 13 / 20 = 0.65

Step 2 : To find P(A')
          P(A') = 1 - 0.65 = 0.35

Multiple Event Probability

Find multiple event probabilitiy, given n(s) = 10, n(A) = 8 and n(B) = 2

Step 1 : To find P(A)
         P(A) = 8 / 10 = 0.8

Step 2 : To find P(A')
          P(A') = 1 - 0.8 = 0.2

Step 3 : To find P(B)
         P(B) = 2 / 10 = 0.2

Step 4 : To find P(B')
          P(B') = 1 - 0.2 = 0.8

Step 5 : To find P(A ∩ B)
         P(A ∩ B) = 0.8 *0.2 = 0.16

Step 6 : To find P(A ∪ B)
         P(A ∪ B) = ( 0.8 + 0.2 ) - 0.16 = 0.84

Step 7 : To find P(A | B)
         P(A | B) = 0.16 / 0.2 = 0.8

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