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March 8th, 2017, 08:17 AM   #1
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Hypergeometric distribution for different probabilities for each draw

The object of my exercise is to calculate the probabilities of different draws from a set, without replacement, but each draw does not have the same probability as the others.

If we use Powerball for example, there are 59 balls and we pick 5 of them.

Using the Hypergeometric distribution, we can calculate the probability of matching 3 of the 5 balls picked.

This is done under the assumption that all balls have equal probability of appearance.

What if the probability of the balls were not equal but were different for each ball? This cannot be described by the Hypergeometric distribution.

How can I calculate the probability of success for a draw, for balls that I chose, given the frequency distribution or probability for the specific balls I choose?

The draws are done without replacement, as in the original hypergeometric distribution

Last edited by mathdudes; March 8th, 2017 at 08:26 AM.
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