Darth Vader is designing a game that costs $20. The game consists of pulling a colored rock out of a container. When the rock is Red Darth Vader pays nothing, when the rock is Blue Darth Vader pays $40, and when the rock is White Darth Vader pays $100.
The first player is Frank and the container contains 8 Red Rocks, 3 Blue Rocks, and 2 White Rocks.
What is the expected value of this game for Darth Vader? What is the expected value of this game for Frank?
13 rocks: 8 red, 3 blue, 2 white
expected value of Red = (8/13)(0) = 0
expected value of Blue = (3/13)($40) = 9.23
expected value of white = (2/13)($100) = 15.38
expected payout = $24.61
Cost of game = $20
Frank should play this game all day long, each time he is expected to win $4.61
Can I play?