Finite math (expected value) word problem

Question

Assume that the fish pond contains 90 fish: 62 blue, 27 silver, and 1 purple. A contestant pays $0.65 to randomly catch one fish and receives $0.30 if the fish is blue, $1.20 if the fish is silver, and $14.00 if the fish is purple. How much on average does the carnival gain on each play

Answer 1

You can find this by finding the expected winnings and then subtracting the 65 cents it costs to play the game. The expected value would just be the sum of each earning level times the probability of that level.

P(blue) = 62/90; P(silver) = 27/90; P(purple) = 1/90

E(earnings) = 0.30*(62/90) + 1.20*(27/90) + 14*(1/90) = $0.78

So the expected gain is 13 cents. (or 13.222 cents if you need some rounding)