Question

A bag contains 2 gold marbles, 8 silver marbles, and 20 black marbles. The rules of the game are as follows: You randomly select one marble from the bag. If it is gold, you win $5, if it is silver, you win $2. If it costs $1 to play, what is your expected profit or loss if you play this game?

Answer 1

expected loss of 4/30 ≈ 0.13 dollars

Explanation:

profit = revenue - expenses

expected profit= expected revenue - expected expenses

how i solve this is by multiplying each revenue and expense by its probability and solving from there

revenue of gold = 5

revenue of silver = 2

revenue of black = 0

this exhausts all of our revenue options

total marbles = 2+8+20 = 30

# of gold marbles = 2

probability of gold = 2/30

# of silver marbles = 8

probability of silver = 8/30

# of black marbles = 20

probability of black = 20/30

expected revenue = sum of possible revenues multiplied by their probability

= 5 * 2/30 + 2 * 8/30 + 0 * 20/30 = 10/30 + 16/30 = 26/30

cost = 1 no matter what

expected profit = expected revenue - expected expenses

= 26/30 - 1

= -4/30

= an expected loss of 4/30

4/30 ≈ 0.13