Answer:
The expected value is -0.5625.
Step-by-step explanation:
Given,
Gold marbles = 1,
Silver marbles = 10,
And, black marbles = 21,
Thus, the total marbles = 1 + 10 + 21 = 32,
So, the probability of gold marble =
Similarly, probability of silver marble =
Probability of black marble =
Now, the value of a gold marble, a silver marble and black marble are $4, $2 and - $2 respectively, ( -$ 2 means loss of $ 2 )
So, expected value of gold = probability of a gold marble × the value of a gold marble =
Similarly,
Expected value of silver marble =
Expected value of black marble =
Hence, the total expected value =