a bag contains 1 gold marbles, 10 silver marbles, and 21 black marbles. someone offers to play this game: you randomly select one marble from the bag. if it is gold, you win $4. if it is silver, you win $2. if it is black, you lose $1.
what is your expected value if you play this game?

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 =  

use formula for the circle a=3.14

step-by-step explanation:

step-by-step explanation:

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