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Cumulative Hypergeometric Distribution
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Definition:
A cumulative hypergeometric distribution is used for calculating the probability of getting atleast n successes in the hypergeometric experiment.
Formula:
h(x < x;N;n;k) = h(x = 0;N;n;k) + h(x = 1;N;n;k) +...+ h(x = x;N;n;k)
where,
h(x = 0;N;n;k) and h(x = x;N;n;k) is calculated using hypergeometric distribution formula.
Example:
Consider, if 5 balls are chosen randomly from the total of 10 balls without repetition. Calculate the probability of getting atleast 2 red balls out of 6 red balls.
where, N=10, n=6, k=5, and x=2.
h(x < 2;N;n;k) = h(x = 0;N;n;k) + h(x = 1;N;n;k) + h(x = 2;N;n;k)
= [5C0] [5C4] / [10C6] + [5C1] [5C4] / [10C6] + [5C2] [5C4] / [10C6]
= 0.001 + 0.024 + 0.238.
= 0.263.
Hence there are 26.3% possibilities for choosing atleast 2 red balls without repetition.
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