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Answer:
expected loss of 4/30 ≈ 0.13 dollars
Step-by-step 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