What is the probability that selects $i$ red ball and $n-i$ green ball, with replacement?

Question

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

Answer 1

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?