Explanation:
the expected value is the sum of all values multiplied by their corresponding probabilities.
and a probability is always
desired cases / totally possible cases.
in the bag are
28 + 6 + 1 = 35 marbles
the probability to pull the gold is
1/35
the probability to pull a silver is
6/35
the probability to pull a black is
28/35 = 4/5
the expected value = $3×1/35 + $2×6/35 - $1×28/35 =
= 3/35 + 12/35 - 28/35 =
= -13/35 = -0.371428571... ≈
≈ -$0.37
that means (like with all games of that kind like all casino games) the bank will win in the long run.
your only chance to win is to play very few times and get a winner by pure chance. the longer you play you might actually hit a winner somewhere in between, but the surer you still lose in total.