random testing model in Python

I would like to use a Poisson test function, whereby an event occurs or not according to a given probability p. Python's random module does not seem to have something like this, thus I figured out

• Turn probability p into a fraction


• randomly pick an integer.


• Success is smaller - or - equal to the numerator from a range of integers equal to the denominator.

I, however believe that this is not the most efficient piece of code for the given task. I also doubt about its correctness, nonetheless I think it shoud be if random.randrange(int) works according to uniform distribution.

def poisson_test(p):

    '''Poisson test with two possible outcomes, where p is success probability'''

    import fractions

    import random

    from decimal import Decimal

    p = Decimal('{0}'.format(p))

    p = fractions.Fraction(p)

    if random.randrange(p.denominator) <= p.numerator :

        return True

    else:

        return False

Any suggestions???

Thanks!