How Do You Calculate Probabilities with Unknown Ball Quantities?

[kecontroversy]

hi guys. I am here again, and facing one of the most difficult question ever faced before. so hope u can help me. below is the question and how I am thinking.


Someone would label the two competing soccer teams as the Red Team and the Green Team. An unknown number of red ping-pong balls, green ping-pong balls, and white ping-pong balls would be put inside a black bag. She would pick up 5 balls randomly from this bag for every minute that the soccer match is in play, and return all 5 balls back into the bag. If she had picked ALL red balls, she would cause a Red Team player to score a goal within that minute. If she picked ALL green balls, she would cause a Green Team player to score a goal within that minute. If she picked ALL white balls, she would cause the soccer match to be abandoned. THE QUESTION ASK ABT THE PROBABILITIES AS NORMAL. [e.g What is the probability that the Red Team will score a goal in anyone minute?]

BUT THE PROBLEM IS I DUN KNOW THE TOTAL NUMBER OF THE BALLS, AND WHETHER THE NUMBER OF RED BALLS AND WHITE BALLS AND GREEN BALLS ARE EQUAL. and TO FIND OUT THE TOTAL NUMBER OF BALLS, DO I HAVE TO USE X AND Y , INSTEAD OF ORDINARY WAY OF CALCULATION, AND I HAVE TO USE ASSUMPTION TO SOLVE THE PROBLEM RIGHT? is there permutation and combination involved?

THANKS..

 

[LeonhardEuler]

The solution will clearly depend on the number of each color ball. My guess is that you are not looking for a numeric solution to this problem, but for expresstions. For example, you could call the # of red balls R, green G, white W. The probability of selecting a green ball is then P = \frac {G} {R+G+W} and the probablity of selecting 5 green balls in 5 tries is P = (\frac {G} {R+G+W})^5

 

[EnumaElish]

[e.g What is the probability that the Red Team will score a goal in anyone minute?]

...

BUT THE PROBLEM IS I DUN KNOW THE TOTAL NUMBER OF THE BALLS, AND WHETHER THE NUMBER OF RED BALLS AND WHITE BALLS AND GREEN BALLS ARE EQUAL.

Is there a conditional prob. involved? For either team to score a goal at time t (0 < t < 90), she must not have picked 5 whites up until that minute. (Such like, with independent coin flips, what is the probability of t heads in a row?)

 

[qbert]

BUT THE PROBLEM IS I DUN KNOW THE TOTAL NUMBER OF THE BALLS, AND WHETHER THE NUMBER OF RED BALLS AND WHITE BALLS AND GREEN BALLS ARE EQUAL. and TO FIND OUT THE TOTAL NUMBER OF BALLS, DO I HAVE TO USE X AND Y , INSTEAD OF ORDINARY WAY OF CALCULATION, AND I HAVE TO USE ASSUMPTION TO SOLVE THE PROBLEM RIGHT? is there permutation and combination involved?

THANKS..

Since you don't know what the numbers are you're going to have
to use variables. (You don't have to call them X and Y tho...)

You can solve this using combinations easily enough. (In fact
you can just write down the answer.) You can also logic your
way through it.

let R = # of red balls, G = # of green balls, and W= # of white balls
now imagine pulling out 5 red balls, one at a time.

the probabillity of pulling out the first is (# of red) / (total #) = R/(R+G+W).
after that one is out how many reds are left?
how many total balls?
what's the probabillity of pulling out the next red?

if you can answer those questions the problem is a breeze.
Oh, and note P(5 reds) = P(1st is a Red) x P(1 red, after you've
taken out 1 Red) x P(1 red, after you've taken out 2 reds)...