Maximum and minimum Expected values when taking colored balls We have a sack with $60$ balls.
From them $15$ balls are red, $15$ green, $15$ blue and $15$ yellow.
We take $30$ balls from the sack.
What's the expected number of balls of the color from which the most balls had been taken? And from the color from which the least balls had been taken?
Expressed in the notation I begun to solve this unsuccesfully:
Let $X_i$ be a random event for the number of balls taken of the color $i$.
I look for: $E[\max(X_1,X_2,X_3,X_4)]$ and $E[\min(X_1,X_2,X_3,X_4)]$
I got that $P(X_i=x)=\frac{\binom{15}{x}\binom{45}{30-x}}{\binom{60}{30}}$

Comment. This plot shows maximum and minimum values from a million runs
of this experiment. Points are randomly 'jittered' $\pm 0.3$
to prevent massive 'overplotting'. A few very rare, but possible
combinations of values at upper-left of the plot did not occur in this particular
simulation. From computations, the respective expected values seem to be about 5.51 and 9.49; the modes are 6 and 9, medians 6 and 9. 
The four $X_i$ of this problem are correlated, so some traditional approaches towards an analytic solution are not available for deriving distributions of the maximum and minimum. Maybe this plot
will suggest possible methods of solution.

