probability
Calculate P(A) = favorable outcomes / total outcomes.
This is the worked example that ships with the calculator. Replace the values above with your own and press Calculate.
FormulaP(A) = favorable outcomes / total outcomesfavorable = 3, total = 12
0.2500
Free reference
Probability rules let you combine and update chances: complements, unions, intersections, conditional probability and Bayes theorem. The two formulas below drive most of the calculators in this category.
P(A | B) = P(A and B) / P(B) - Probability of A after restricting attention to cases where B occurred.P(A | B) = P(B | A)P(A) / P(B) - Updates a prior probability after observing evidence.In a class, 12% of students both take statistics and play a sport, and 30% of students play a sport. Given that a student plays a sport, what is the probability they take statistics?
Inputs. P(A and B) = 0.12, P(B) = 0.30.
P(A|B) = P(A∩B) / P(B) gives P(A∩B) = 0.1200, P(B) = 0.3000P(A|B) = 0.1200 / 0.3000 gives 0.4000Answer: 0.4
Restricting attention to the 30% who play a sport, the 12% who do both make up 0.12 / 0.30 = 0.4, so a sporty student has a 40% chance of taking statistics.
P(A given B) is the probability of A after restricting attention to the cases where B occurred. It is computed as P(A and B) divided by P(B), exactly as in the worked example above: 0.12 / 0.30 = 0.4.
Use Bayes theorem when you know P(B given A) but need P(A given B), that is, when you want to reverse the direction of the conditioning. It rescales the prior probability of A by how strongly B points to A.
The probability that an event does not happen is 1 minus the probability that it does: P(not A) = 1 - P(A). It is often easier to compute the complement first, for example the chance of at least one success.