Probability of picking something Let's say there are 12 red 11 green 12 yellow marbles. I pick up 7 marbles randomly. What's the probability of me picking 2 red marbles?
I understand the probability of picking up a red marble is 12/35. How does this relate to picking up 7 marbles and ending up with 2 red ones? I would like an explanation, not just the answer, please.

you need exactly $2$ red marbles out of $7$ you chose from a set of $12$ red, $11$ green and $12$ yellow.
No. of ways to choose $2$ red marbles out of $12$ marbles (red)$={12\choose 2}$
No. of ways to choose remaining $5$ marbles out of $23$ marbles (non-red)= ${23\choose 5}$
Total ways of choosing $7$ marbles out of $35$ marbles =${35\choose 7}$
Therefore, Required  Probability = $$\frac{{12\choose 2}{23\choose 5}}{{35\choose 7}}$$
