4 red, 3 blue, 2 yellow, and 1 green marble:
Gives total marbles of 10
First pick probability for any of our marbles:
Red: 4/10
Blue: 3/10
Yellow: 2/10
Green: 1/10
(4 + 3 + 2 + 1 = 10, which is our total, the marbles are over btw)
without replacement means it's (the marbles picked) not being put back after picking, so, total marbles drop down.
E.g. I have 5 orange, I take one without replacements. This means I must have 4 oranges in total now.
Second pick:
Lets say I get red, next pick:
probability is now over 9 due to no replacement:
Red: 3/9
Blue: 3/9
Yellow: 2/9
Green: 1/9
(3 + 3 + 2 + 1 = 9, which is our new total.)
So, total red drops down from 4 to 3, on our second pick. The rest remains the same due to not being picked
Thus, probability of picking the red red will be:
First pick x second pick
4/10 x 3/9 = 12/90
You don't need to simplify, if you do, you get the equivalent fraction of 2/15 for the probability.
Ans: 12/90 (or 2/15)
Hope this helps!
