A bag contains 3 gold marbles 7 silver marbles and 27 black

A bag contains 3 gold marbles, 7 silver marbles, and 27 black marbles. Someone offers to play this game: You randomly select on 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?

$

Solution

Bag contains total 37 marbles: 3 gold, 7 silver, 27 black

E= 4(3/37) + 2(7/37) - 1(27/37)

= 12/37 + 14/37 - 27/37

= -1/37

= -0.027