I’m trying to use scipy in order to calculate a probability, given a binomial distribution:
The probability: in an exam with 45 questions, each one with 5 items, what is the probability of randomly choose right (instead of wrong) more than half the exam, that is, 22.5?
I’ve tried:
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from scipy.stats import binom2
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n = 454
p = 0.205
mu = n * p 6
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p_x = binom.pmf(1,n,p)8
How do I calculate this with scipy?
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Answer
Assuming there’s exactly one correct choice for each question, the random variable X which counts the number of correctly answered questions by choosing randomly is indeed binomial distributed with parameters n=45 and p=0.2. Hence, you want to calculate P(X >= 23) = P(X = 23 ) + ... + P(X = 45 ) = 1 - P(X <= 22), so there are two ways to compute it:
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from scipy.stats import binom2
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n = 454
p = 0.25
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# (1)7
prob = sum(binom.pmf(k, n, p) for k in range(23, 45 + 1))8
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# (2)10
prob = 1 - binom.cdf(22, n, p)11