# Estimate a probability with Monte Carlo¶

In this example we estimate a probability by means of a simulation algorithm, the Monte-Carlo algorithm. To do this, we need the classes MonteCarloExperiment and ProbabilitySimulationAlgorithm. We consider the axial stressed beam example.

```from __future__ import print_function
from openturns.usecases import stressed_beam as stressed_beam
import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
ot.Log.Show(ot.Log.NONE)
```

We load the model from the usecases module :

```sm = stressed_beam.AxialStressedBeam()
```

We get the joint distribution of the parameters.

```distribution = sm.distribution
```

The model is also stored in the data class :

```model = sm.model
```

We create the event whose probability we want to estimate.

```vect = ot.RandomVector(distribution)
G = ot.CompositeRandomVector(model, vect)
event = ot.ThresholdEvent(G, ot.Less(), 0.0)
```

Create a Monte Carlo algorithm.

```experiment = ot.MonteCarloExperiment()
algo = ot.ProbabilitySimulationAlgorithm(event, experiment)
algo.setMaximumCoefficientOfVariation(0.05)
algo.setMaximumOuterSampling(int(1e5))
algo.run()
```

Retrieve results.

```result = algo.getResult()
probability = result.getProbabilityEstimate()
print('Pf=', probability)
```

Out:

```Pf= 0.02936292270531395
```

Total running time of the script: ( 0 minutes 0.103 seconds)

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