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I have a question as below: Let there be 3 groups of people, Group A (60%), B(25%), and C(15%) of the whole population. What is the expected probability that a person from Group A will randomly meet a person from Group A, Group B, and Group C, respectively?

I came up with this question in a social study I am doing recently. I'm not a mathematician, so what I thought is quite simple but I am not sure if it is correct. Please provide your opinion, and do feel free to make assumptions or conditions for solving the question if it is neccessary.

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If you mean the next person she meets, the probabilities are $60\%$, $25\%$. $15\%$, with slight correction if the population is very small, like $12,5,3$ since someone cannot meet herself. If there are several interactions, the question should be altered, like "Among the next $4$ people she meets, what is the probability at least one is a C? – André Nicolas Feb 18 '13 at 12:40
Thanks very much for your responses. The answers look quite straightforward. I totally agree with the first person how the "meeting" process takes place should be specified. Hence, when it comes to the probability of 2 Groups meeting with each other (undirected), the second answer is appropriate. – user63104 Feb 20 '13 at 9:29

P(G1 & G1) = P(G1) ^2 P(G2 & G2) = P(G2) ^2 P(G3 & G3) = P(G3) ^2 P(G1 & G2) = 2*P(G1)*P(G2) P(G1 & G3) = 2*P(G1)*P(G3) P(G2 & G3) = 2*P(G2)*P(G3)

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You may want to edit this so it's a bit more readable. – mrf Feb 18 '13 at 15:43

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