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Probability

The Wolfram Language contains a wide range of functions for probability, as well as hundreds of symbolic distributions.

Calculate factorials using mathematical notation:

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5!
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For combinations, use Binomial:

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Binomial[4, 3]
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Compute probabilities for a binomial distribution:

(Type ESCdistESC for the symbol.)
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⨯ 
Probability[x == 1, x \[Distributed] BinomialDistribution[1, 1/2]]
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Calculate the expectation of a polynomial expression:

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Expectation[2 x + 3, x \[Distributed] NormalDistribution[]]
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Get the PDF for a normal distribution in symbolic form:

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PDF[NormalDistribution[0, 1], x]
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Make a Plot of the result:

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Plot[%, {x, -5, 5}, Filling -> Axis]
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Free-form input can be used to calculate the probability of real-world events:

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birthday problem 18 people
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QUICK REFERENCE: Combinatorial Functions »

QUICK REFERENCE: Probability & Statistics »