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## Main Question or Discussion Point

Suppose r red balls and g green balls are mapped randomly among b bins. Calculate the expected number of bins where red balls are in majority.

My attempt,

Let x_ijk

= 1 (when kth bin contains i red balls and j green balls)

= 0 otherwise

Then,

F = [tex]\sum_{k=1}^{b} \sum_{i=1}^{r} \sum_{j=0}^{i-1} x_{ijk}[/tex]

Then i calculated E[F]

with E[x_ijk]= (1/b)^(i+j) .. (*)

The final answer is completely in terms of b and r alone and this is quite suspicious. I expect g to be in the expression.

I think i am making some obvious mistake but what is it or is it a mistake at all is something which i am not able to identify.

-- AI

My attempt,

Let x_ijk

= 1 (when kth bin contains i red balls and j green balls)

= 0 otherwise

Then,

F = [tex]\sum_{k=1}^{b} \sum_{i=1}^{r} \sum_{j=0}^{i-1} x_{ijk}[/tex]

Then i calculated E[F]

with E[x_ijk]= (1/b)^(i+j) .. (*)

The final answer is completely in terms of b and r alone and this is quite suspicious. I expect g to be in the expression.

I think i am making some obvious mistake but what is it or is it a mistake at all is something which i am not able to identify.

-- AI