Question

HELP

Answer 1

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Answer 2

In a carnival game, a player selects balls one at a time (without replacement) from an urn containing 2 red and 4 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. Write down the probability distribution for the player's earnings

Answer 3

i need to know the logic behind each probability for each earning

Answer 4

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

Answer 5

okay but how did you find each probability?

Answer 6

P(r) | 1/3 4/15 1/5 2/15 1/15
Then \[\mu=-\frac{ 0.50 }{ 3 }+0+\frac{ 0.50 }{ 5 }+\frac{ 2 }{ 15 }=0.166666.....=0.17\] 17 is his expected earnings