Question 1099881: A carnival operator is constructing a new game.
In this game, the player will place a bet. Then a ball is selecteded from an urn containing balls of three colours: 2 green balls, 4 red balls and 7 white balls.
If a red ball is drawn, the player wins 1$, if a green ball is drawn, the player wins 4$, and if a white ball is drawn the player wins nothing.
What should the carnival operator set the bet at such that on average he makes $0.50 profit a game? (That is, so the player loses $0.50)
Answer by greenestamps(13215)   (Show Source):
You can put this solution on YOUR website!
The average payout is the sum of all the products obtained by multiplying the probability of an event times the payout for that event.
There are 13 balls -- 2 green, 4 red, and 7 white. The probability of getting a green is 2/13, red 4/13, and white 7/13.
The payout is $1 for red, $4 for green, and $0 for white.
The average payout is then 
The average payout is 12/13 dollars. If the operator wants on average to get 1/2 dollar profit per game, the cost for playing the game needs to be  approximately.
The operator can't charge a dollar and 42.3 cents (approximately) to play the game.
So with the numbers given in the problem, the problem is poorly constructed; I'm not sure what the answer to the question is supposed to be.
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