SOLUTION: In a carnival game the player selects balls one at a time, without replacement, from a urn containing two red and four white balls. The game proceeds until a red ball is drawn. T

Question 379527: In a carnival game the player selects balls one at a time, without replacement, from a urn containing two red and four white balls. The game proceeds until a red ball is drawn. The player pays $1 to play the game and receives $0.50 for each ball drawn. Contruct a probability distribution table for the player's earnings for this game and find a player's expected value for this game.
I do not have a clue how to do this, please helppppp.. The answer is $0.17, but how...

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let R = random variable representing the player's earnings for this game.
The elements of the sample space of drawings are {r, wr, wwr, wwwr, wwwwr}
The probability of the outcome r is 1/3. The earning is 0.50-1 = -0.50.
The probability of the outcome wr is 4/15. The earning is 2*0.50 - 1 = 0.
The probability of the outcome wwr is 1/5. The earning 3*0.50 - 1 = 0.50.
The probability of the outcome wwwr is 2/15. the earning is 4*0.50 - 1 = 1.00.
The probability of the outcome wwwwr is 1/15. The earning is 5*0.50 - 1 = 1.50.
R=r | -0.50 0 0.50 1.00 1.50
--------------------------------------------------
P(r) | 1/3 4/15 1/5 2/15 1/15
Then , or $0.17, his expected earnings.
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