A box contains 3 red balls, 4 blue balls, and 6 green balls. Balls are drawn one-by-one without replacement until all the red balls are drawn. Let $D$ be the number of draws made.
Calculate:
a)$P(D\le 9)$
b)$P(D=9)$
c)$E(D)$
For part a) I know the answer should be $\binom{10}{6}/\binom{13}{9}$ but not sure how to get this.
And I am wondering the relationship between (a) and (b). And how to calculate hypergeometric distribution in general.
For part c) I could use the basic definition to get the answer but I am sure there is an easier way to do this.