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from scipy.special import binom
import scipy.stats
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# scipy.stats.binom.pmf(x, n, p)
# scipy.stats.hypergeom.pmf(k, M, n, N)
Suppose you have an urn that contains 30 red and 60 blue marbles.
Consider "sampling without replacement". If you draw 5 marbles at once (without putting them back) what is the probability that 3 are blue?
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scipy.stats.binom.pmf(3, 5, 2/3)
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N = 90
K = 60
n = 5
k = 3
binom(K, k) * binom(N-K, n-k) / binom(N, n)
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# scipy.stats.hypergeom.pmf(k, N, K, n)
# N: marbles in urn
# K: marbles considered success
# n: number selected
# k: number of successes
N = 90
K = 60
n = 5
k = 3
scipy.stats.hypergeom.pmf(k, N, K, n)
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