Question

Assume that the pond contains 90 fish: 64 purple, 25 green, and 1 red. A contestant pays $0.55 to randomly catch one fish and receives $0.40 if the fish is purple, $1.15 if the fish is green, and $9.00 if the fish is red. How much (on average) does the carnival gain on each play? (If the carnival looses money, enter a negative dollar amount)

Answer 1

The carnival is losing (on average) $0.15 on each play

Explanation:

To find out how much the carnival wins or looses in each play one subtract the expected value (EV) from each play from the amount charged by the carnival for each play ($0.55). If the expected value is higher than what the carnival charges, the carnival is losing money.

Expected is the sum of the payouts of each bet multiplied by its likelihood:

`EV= (64*0.40+25*1.15+1*9.00)/(90)\\EV= 0.70`

Since the expected value is higher than $0.55, the carnival is losing money, on average, on each play:

`0.55-0.7 = -0.15`

The carnival is losing (on average) $0.15 on each play