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42 lines
1.5 KiB
Python
42 lines
1.5 KiB
Python
"""For more information about the Binomial Distribution -
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https://en.wikipedia.org/wiki/Binomial_distribution"""
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from math import factorial
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def binomial_distribution(successes: int, trials: int, prob: float) -> float:
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"""
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Return probability of k successes out of n tries, with p probability for one
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success
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The function uses the factorial function in order to calculate the binomial
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coefficient
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>>> binomial_distribution(3, 5, 0.7)
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0.30870000000000003
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>>> binomial_distribution (2, 4, 0.5)
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0.375
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"""
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if successes > trials:
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raise ValueError("""successes must be lower or equal to trials""")
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if trials < 0 or successes < 0:
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raise ValueError("the function is defined for non-negative integers")
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if not isinstance(successes, int) or not isinstance(trials, int):
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raise ValueError("the function is defined for non-negative integers")
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if not 0 < prob < 1:
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raise ValueError("prob has to be in range of 1 - 0")
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probability = (prob**successes) * ((1 - prob) ** (trials - successes))
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# Calculate the binomial coefficient: n! / k!(n-k)!
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coefficient = float(factorial(trials))
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coefficient /= factorial(successes) * factorial(trials - successes)
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return probability * coefficient
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if __name__ == "__main__":
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from doctest import testmod
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testmod()
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print("Probability of 2 successes out of 4 trails")
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print("with probability of 0.75 is:", end=" ")
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print(binomial_distribution(2, 4, 0.75))
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