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I have $k_1$ red balls and $k_2$ green balls in a box. These balls are select by a uniform distribution. Randomly select $n$ balls from the box with replacement. What is the probability that selects $i$ red ball and $n-i$ green ball?

Note that, the prob. did not follow by Hypergeometric distribution because I am considering the with replacement case.

Thank all

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Note that, the prob. did not follow by Hypergeometric distribution because I am considering the with replacement case.

Correct; it does not do so.   The count of red balls drawn with replacement is the count of 'successes' among a series of $n$ independent and identical Bernoulli events, each with success rate of $k_1/(k_1+k_2)$.   What kind of distribution does that have?

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  • $\begingroup$ Thank Graham Kemp. Is it uniform distribution? $\endgroup$ – Jame Aug 28 '16 at 10:44
  • $\begingroup$ @user2938494 No. Very definitely not. $\endgroup$ – Graham Kemp Aug 29 '16 at 6:23
  • $\begingroup$ Or maybe it is binomial distribution? $\endgroup$ – Jame Aug 29 '16 at 6:24

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