Thought process improvement on Probabilities

[cdux]

I had a problem that said "I throw nine balls randomly in five containers. What's the probability any container will have exactly five balls by the end of the process?"

The answer involved using a Binomial distribution.

Now the question is, how do I train my mind to go to the use of distributions and not basic Kolmogorov probability functions? I was spending so much time trying to find a simple answer and I was surprised it was easier with a binomial distribution. What is the right thought process to easily direct me to the use of a distribution in that problem?

 

[mathman]

Use a multinomial distribution.

http://en.wikipedia.org/wiki/Multinomial_distribution

 

[D H]

Now the question is, how do I train my mind to go to the use of distributions and not basic Kolmogorov probability functions?

The same way you trained your mind *not* to use the epsilon-delta definition of the derivative.

That limit concept is absolutely essential to making the concept of the derivative rigorous. That doesn't mean you need to use it to compute (for example) the derivative of exp(-x²/2). It's too much work.

The Kolmogorov axioms are similarly essential to making the concept of probability rigorous. That does not mean you should go to first principles and use those axioms to solve every probability problem.

 

[cdux]

Yes, but why should you not go there? I deal with a list of questions that may use basic principles or they may not use basic principles. I'm trying to find out why on that particular question for example I couldn't automatically think of using a distribution.