The Probability command computes the probability of the event X.

The first parameter, X, is an event consisting of a relation or set of relations. An algebraic expression is interpreted as an equation set to zero. Each relation must involve at least one random variable. All random variables in X are considered independent. A set is interpreted as the intersection of the events of each of its members.

By default, all computations involving random variables are performed symbolically (see option numeric below).

For more information about computation in the Statistics package, see the Statistics[Computation] help page.

The options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[RandomVariables] help page.

numeric=truefalse -- By default, the probability density function is computed using exact arithmetic. To compute the probability density function numerically, specify the numeric or numeric = true option.

$\mathrm{with}\left(\mathrm{Statistics}\right)\:$

$X≔\mathrm{RandomVariable}\left(\mathrm{Normal}\left(0\,1\right)\right)\:$

$\mathrm{Probability}\left(X^2<1\right)$

$\mathrm{erf}\left(\frac{\sqrt{2}}{2}\right)$

$\mathrm{Probability}\left(X^2<1\&comma;'\mathrm{numeric}'\right)$

$0.682689492137086$

$X≔\left[\mathrm{seq}\left(\mathrm{RandomVariable}\left(\mathrm{Uniform}\left(0\&comma;1\right)\right)\&comma;i=1..4\right)\right]\&colon;$

$Y≔X\left[1\right]X\left[2\right]X\left[3\right]\&colon;$

$\mathrm{Probability}\left(Y<t\right)$

$\left\{\begin{array}{cc}0& t\le 0\\ \frac{{\ln \left(t\right)}^{2}t}{2}-t\ln \left(t\right)+t& t\le 1\\ 1& 1<t\end{array}\right.$

$Z≔{\left({\left(X\left[1\right]-X\left[3\right]\right)}^2+{\left(X\left[2\right]-X\left[4\right]\right)}^2\right)}^{\frac{1}{2}}\&colon;$

$\mathrm{Probability}\left(Z<\frac{1}{2}\right)$

$-\frac{29}{96}+\frac{\mathrm{\pi }}{4}$

Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.