[Brandonb]

I misinterpreted brhan's "colored ball" post and accidentally came up with this. I believe it is much simpler but still entertaining.

Billy put a number of different colored balls (ex. 2 blue, 5 red, 1 purple, 7 green...) in a box. After a while he added 20 more balls (all of the same color as one color already in the box) to the box, and the addition of the new balls did not change probability of drawing two balls of the same color (with replacement).

How many different colors of balls are in the box? And how many of each color were in the box originally?

[Guest]

umm, i might be totally off, but were there five 1 of each of 20 dif colors, then added 1 more of each color? or maybe im totaly wrong like i said.

[Yoruichi-san]

Umm...

There is only one color. So the probability of getting a pair is always one. Otherwise, I don't know if it is possible...

The probability of getting the a pair is (A/N)^2+(B/N)^2+(C/N)^2...=(A^2+B^2+C^2...)/(N^2)

where A,B,C...represent the numbers of the different colors, and N is the total number of balls.

Adding 20 balls of color A makes the probability: (A+20)^2/(N+20)^2+B^2/(N+20)^2+C^2/(N+20)^2...=(A^2+40A+400+B^2+C^2...)/(N^2+40N+400)

which only equals the original probability (for real positive integers)if A=N and B=C=D=E=...=0.

Edited June 19, 2008 by Yoruichi-san

[Guest]

Umm...

There is only one color. So the probability of getting a pair is always one. Otherwise, I don't know if it is possible...

The probability of getting the a pair is (A/N)^2+(B/N)^2+(C/N)^2...=(A^2+B^2+C^2...)/(N^2)

where A,B,C...represent the numbers of the different colors, and N is the total number of balls.

Adding 20 balls of color A makes the probability: (A+20)^2/(N+20)^2+B^2/(N+20)^2+C^2/(N+20)^2...=(A^2+40A+400+B^2+C^2...)/(N^2+40N+400)

which only equals the original probability (for real positive integers)if A=N and B=C=D=E=...=0.

That's what I was thinking.

[Brandonb]

Wow, must first post, lol. As expected it was flawed, I'm sure there could be different answers to it. Anyway, this was a rough draft for what turned out to be Balls in a box #3 sorry