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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:

 In[1]:= ⨯ `5!`
 Out[1]=

For combinations, use Binomial:

 In[2]:= ⨯ `Binomial[4, 3] `
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Compute probabilities for a binomial distribution:

(Type ESCdistESC for the `` symbol.)
 In[1]:= ⨯ `Probability[x == 1, x \[Distributed] BinomialDistribution[1, 1/2]]`
 Out[1]=

Calculate the expectation of a polynomial expression:

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

 In[1]:= ⨯ `PDF[NormalDistribution[0, 1], x]`
 Out[1]=

Make a Plot of the result:

 In[2]:= ⨯ `Plot[%, {x, -5, 5}, Filling -> Axis]`
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Free-form input can be used to calculate the probability of real-world events:

 In[1]:= X `birthday problem 18 people`
 Out[1]=

QUICK REFERENCE: Combinatorial Functions `»`

QUICK REFERENCE: Probability & Statistics `»`