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 = [tex]\frac{\text{ gold marble}}{\text{total marbles}}=\frac{1}{32}[/tex]
Similarly, probability of silver marble = [tex]\frac{10}{32}[/tex]
Probability of black marble = [tex]\frac{21}{32}[/tex]
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 = [tex]4(\frac{1}{32})[/tex]
Similarly,
Expected value of silver marble = [tex]2(\frac{10}{32})[/tex]
Expected value of black marble = [tex]-2(\frac{21}{32})[/tex]
Hence, the total expected value = [tex]4(\frac{1}{32})+2(\frac{10}{32})+-2(\frac{21}{32})[/tex]
[tex]=-0.5625[/tex]
