Calculating Probability for Multiple Buckets: Tips and Tricks

[flying2000]

How to calculate the probability of this questions?

Supposed there are m bukcets, n balls. use function f(x) to decide which bucket the ball go. Supposed that the probability a ball going to 0-j is 0.9 and going to j -> m-1 is 0.1. What's the probability of for every bucket there is at least one ball?

I really get stuck.

Any help appreciated!

 

[HallsofIvy]

I do not understand what you mean by "a ball going to 0-j" or "going to j -> m-1 ". I presume that you have the buckets labeled 1 to m by "m-1" you mean the bucket labeled that way- but what is j?

 

[flying2000]

I do not understand what you mean by "a ball going to 0-j" or "going to j -> m-1 ". I presume that you have the buckets labeled 1 to m by "m-1" you mean the bucket labeled that way- but what is j?

Yes, the buckets are labeled from 0 to m-1,
the probaiblity that a ball going to buckets(from 0 to j-1) is 0.9, and going to j-1 to m-1 bucket is 0.1. and inside [0, j-1] and [j-1, m-1] is equally. j is only a number. for example if m=4, j=2 and p(a ball go to bucket 0,1) = 0.9 and p(go to bucket 2,3)=0.1

 

[Tide]

HINT: Calculate the probability that a bucket contains no balls - it is a binomial distribution.

Also, are you sure the two bucket ranges overlap??

 

[flying2000]

HINT: Calculate the probability that a bucket contains no balls - it is a binomial distribution.
Also, are you sure the two bucket ranges overlap??

Thanks a lot. Yes I made a mistake here, the latter should be j -> m-1.
Your advice is really helpful..