You draw two marbles at random from a jar that has 20 red marbles and 30 black marbles without replacement. what is the probability that both marbles are red?

Ok so we know there are 20 red marbles and 30 black marbles, meaning when you draw the first marble, there are 20 out of 50 possible marbles which we "want".
Hence the chance of obtaining a red marble the first time is 20/50, or a 2/5 chance.

For the second draw, we aren't replacing the marble, but we assume that we successfully drew the red marble in the first draw, so now there are 19 out of 49 marbles which we want, or a 19/49 chance.

This means the probability of drawing 2 red marbles in a row is:
[tex] \frac{2}{5} \times \frac{19}{49} [/tex]
Which is a
[tex] \frac{38}{245} [/tex]
chance.

Hope this helps in some way.