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Basic Statistics: Probability distribution for sampling 100 subjects belonging to 4 equally proportioned categories out of 400 subject population ?

Hi JMP Community,

I need to estimate the probability of sampling different proportion of 100 subjects out of a 400 population belonging to 4 equally proportioned categories

I used a simple binomial distribution approach but I'm not sure that it is the correct method. Here is the specifics about my questions

Population: N = 400

Group A: 25%

Group B: 25%

Group C: 25%

GroupD:25%

==> what is the chance of having group A represented by less than 10 subject AND of having Group B represented by less than 10 patients in a sample of 100?

The main issue that the actual sample number for one group influences the other groups: how do I account for that?

Thanks for your help.

Best,

Analytics

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