Answer:
First, we have two marbles, and i guess that each one has the same probability of being picked at random (actually they have different densities, so one may have a larger probability than the other).
The possible outcomes are:
S G
S S
G S
G G
Now, suppose that we want to find the probability of the S G outcome.
In the first selection, we want to pick the silver marble, with a probability of ps,
In the second selection, we want to pick the gold marble, with a probability pg
As the events are independent, the joint probability will be equal to the product of the probabilities for each selection:
P = ps*pg
Now, if both marbles have the same probability of being picked, then:
ps = 0.5
pg = 0.5
P = 0.5*0.5 = 0.25
And this will be the same for each outcome.