Question 349773
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.