BUILT-IN MATHEMATICA SYMBOL

NProbability

NProbability[pred, xdist]
gives the numerical probability for an event that satisfies the predicate pred under the assumption that x follows the probability distribution dist.

NProbability[pred, {x₁, x₂, ...}dist]
gives the numerical probability that an event satisfies pred under the assumption that follows the multivariate distribution dist.

NProbability[pred, {x₁dist₁, x₂dist₂, ...}]
gives the numerical probability that an event satisfies pred under the assumption that , , ... are independent and follow the distributions , , ....

NProbability[pred₁pred₂, ...]
gives the numerical conditional probability of given .

Details and Options Details and Options

can be entered as x EscdistEsc dist or .
can be entered as EsccondEsc or .
NProbability works like Probability except numerical summation and integration methods are used.
For a continuous distribution dist, the probability of pred is given by where is the probability density function of dist and the integral is taken over the domain of dist.
For a discrete distribution dist, the probability of pred is given by where is the probability density function of dist and the summation is taken over the domain of dist.
NProbability[pred, {x₁dist₁, x₂dist₂}] corresponds to NProbability[NProbability[pred, x₂dist₂], x₁dist₁] so that the last variable is summed or integrated first.
N[Probability[...]] calls NProbability for probabilities that cannot be done symbolically.
The following options can be given:

AccuracyGoal	∞	digits of absolute accuracy sought
PrecisionGoal	Automatic	digits of precision sought
WorkingPrecision	MachinePrecision	the precision used in internal computations
Method	Automatic	what method to use