Recent content by paolopiace

Thank You. That's nice. But it's not what the original problem asks. It states and asks: After having thrown R balls over M buckets, the probability that exactly n<R balls fall in one specific bucket is: $$P(X=n)={R \choose n}\left(\frac{1}{M}\right)^n\left(1-\frac{1}{M}\right)^{R-n}$$ That...

Wow... I see. So, let's put the problem (the very 1st post of this thread) a bit differently. Instead of asking "what is the probability to find n red balls into ANY bucket", I ask: "What is the probability to find exactly n red balls into at least one bucket". Here is the train of thoughts...

Thank You! Would you help me with the problem in my original post, here at the top? I really need that probability.

Hummm... Are you sure? So, if I have M=3 buckets and I throw R=2 red balls above them the prob. of finding n=1 red ball in one specific bucket is (from the binomial formula): P(X=1) = 0.444 Based on what you said, M x P(X=1) = 1.333 This is not a probability.

Thank You! It's what I though but I needed confirmation.

Greetings. I would need help as follow up to the answers to my http://mathhelpboards.com/basic-probability-statistics-23/prob-red-ball-buckets-binomial-17282-post79735.html#post79735. After having thrown R red balls over M buckets, the probability that exactly n red balls fall in one, specific...

This is beautiful! I want to thank you so much, although I still have to digest it entirely. Sorry for this late feedback. Many things of life kept me away from my post.

It's 1-1/M I am kind of confused. If a throw R balls in the air, there are R/M probabilities that a specific bucket gets a ball. Or not? 1/M is the probability that a specific bucket gets a ball if I throw one and only one ball. Or nor?

I think there are R/M probabilities to see one red ball in a particular bucket. Then, there are (R-1)/M probabilities to see a second red ball in that same bucket. Therefore R(R-1)/M^2 is the prob. to find two red balls in a particular bucket. Kind of right? Or not?

I know for many of you this sounds trivial. For me it's not... A barrel contains M buckets each containing B balls, for a total of N = M x B balls. N is a big number. A small number R > 1 of balls are red. All the others N-R are white. The location of each one of these R balls is random...