SOLUTION: Three balls are randomly chosen from an urn containing 3 white, 3 red, and 5 black balls. suppose that we win #1 for each white ball selected and lose #1 for each red ball selected

Algebra.Com
Question 1119461: Three balls are randomly chosen from an urn containing 3 white, 3 red, and 5 black balls. suppose that we win #1 for each white ball selected and lose #1 for each red ball selected. what is the probability that we win the money?
Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Three balls are randomly chosen from an urn containing 3 white, 3 red, and 5 black balls. suppose that we win #1 for each white ball selected and lose #1 for each red ball selected. what is the probability that we win the money?
------
Determine # of ways to "win"::
3white:: 1 way
2white and 1red:: 3C2*3C1 = 3*3 = 9 ways
2white and 1black:: 3C2*5C1 = 3*5 = 15 ways
1white and 2black:: 3C1*5C2 = 3*10 = 30 ways
----
Determine # of possible triples:: 11C3 = (11*10*9)/(1*2*3) = 165
------
Ans:: (1+9+15+30)/165 = 55/165
--------
Cheers,
Stan H.
-----------
Answer by ikleyn(52835)   (Show Source): You can put this solution on YOUR website!
.
Since the number of white balls is the same as the number of red balls, 


the game is totally symmetric. In other words, for any combination  (mW,nR) of having m White balls and n Red balls,


there is the same probability to have symmetric combination (nW,mR).


It means that for every chance to win (m-n) dollars, there is THE SAME chance to loose (m-n) dollars.


If the game is repeating infinitely long, the probability to gain money is ZERO - same as the probability to loose money.


The answer and the solution are clear without any calculations.


RELATED QUESTIONS

There are 3 urns containing 2 white and 3 black balls, 3 white and 2 black balls and 4... (answered by richwmiller)
An urn contains six red balls, five white balls, and four black balls. Three balls are... (answered by reviewermath)
A urn contains n black balls and n white balls. Three balls are chosen from the urn at... (answered by math_helper)
There are three urns that each contain 10 balls. The first contains 3 white balls and 7... (answered by scott8148)
An urn contains six red balls, five white balls, and four black balls. Four balls are... (answered by Fombitz)
there are 3 boxes containing respectively 1 white, 2 red, 3 black balls; 2 white, 3 red,... (answered by Theo)
Urn 1 contains 6 red balls and 5 black balls. Urn 2 contains 3 red balls and 3 black... (answered by Boreal)
An urn contains 3 red and 2 white numbered balls. A sample of 2 balls is randomly chosen. (answered by stanbon)
sirs, please help me regarding this problem: "there are 3 urns containing several... (answered by Fombitz)