gistfile1.py

def bayes(a, b_given_a, b_given_not_a):
    """Calculates P(a|b) using bayes theorem.

    Bayes theorem states that:

                       P(b|a) * P(a)
    P(a|b) = --------------------------------
              P(b|a) * P(a) + P(b|~a) * P(~a)

    Intuitively this is saying that the probability of b given a is equivalent
    to the number of times both b and a occur over the number of time b occurs.
    """
    b_and_a = a * b_given_a
    b_and_not_a = b_given_not_a * (1 - a)
    return b_and_a / (b_and_a + b_and_not_a)

if __name__ == "__main__":
    a = input("P(a): ")
    b_given_a = input("P(b|a): ")
    b_given_not_a = input("P(b|~a): ")
    print bayes(a, b_given_a, b_given_not_a)