Question 349773: There are three barrels and each barrel contains an equal number of red, blue, green and yellow balls, The balls are buried in sawdust so that people cannot see them. You win by choosing 3 of the same color balls. You choose a ball from each barrel. $1.00 per game. 3 balls of the same color wins $20.
1. How many different ways are there of choosing the three balls from the barrels? Order matters.
2. How many of them are wins?
3. What is the probability of winning on one turn?
4 Do you think the game will make money? And how much will she expect to win or lose.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 3 barrels
each contains equal number of r, b, g, y balls.
probability of getting all 3 of the same color is?
p of getting first ball is equal to 1
p of getting second ball the same color is .25
p of getting third ball the same color is .25
probability of getting 3 of the same color is 1 * .25 * .25 = .0625
p of all red = .25 * .25 * .25 = .015625
p of all blue = .25 * .25 * .25 = .015625
p of all green = .25 * .25 * .25 = .015625
p of all yellow = .25 * .25 * .25 = .015625
p of either red or blue or green or yellow = 4 * .015625 = .0625
the total different ways of choosing a ball from each barrel would be:
4 * 4 * 4 = 64
the possible ways to win would be 4 * 1 * 1 = 4
winning means either all red, or all green, or all blue, or all yellow.
the probability of getting a win would be 4/64 = .0625
the probability of winning on any one turn is .0625.
if the probability of winning on any one turn is .0625, then the probability of losing on any one turn is 1 - .0625 = .9375.
if the bet is 1 dollars, then every 16 times, you will win once and lose 15 times.
your total loss for the 16 times at bat is 15 dollars.
your total winning has to be 15 dollars for you to break even.
the pot, therefore, needs to be 15 dollars in order for you to break even.
mathematically that comes out to be .9375 / .0625 = 15.
in English, that means the pot should be equal to the probability of losing divided by the probability of winning in order to break even.
if the pot is more than that, then you have the advantage.
if the pot is less than that, then the person running the game has the advantage.
since, in this case, the pot is 20 dollars, you have the advantage and the person running the game has the disadvantage.
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