Problem to resolve these probabilities

[bagheera]

I need to resolve the following problem:

There are 6 buckets and each bucket can hold a maximum of 16 balls. There are 48 balls that need to be located. Assuming that the balls can go everywhere with the same probability.

1.- How much is the probability to have an empty bucket?
2.- How much is the probability to have 2 empty buckets?
3.- Assuming that those 48 balls have to be located sequentially (in 3 consecutive buckets). Answer the questions 1 and 2.

Thanks in advance!!

 

[mmm4444bot]

I need to resolve the following problem

Please explain for us why you're stuck. Or, show your work, thus far. Or, ask specific questions. Or, explain what you're thinking about this exercise, thus far.

Please read the post titled, "Read Before Posting". The information in that post explains how to properly ask for help here.

The boards at FreeMathHelp do not comprise an on-line classroom. Volunteers are here to help you with specific questions about what you don't understand in your lessons or lectures. We can't know what you need, until you tell us.

Cheers ~ Mark

 

[bagheera]

Thanks Mark for your advice. I was trying for a couple of days before asking in the Forum but I was not very happy with my conclutions . I hope you could help me with it.

Initially I tried to answer the 1st question: "what is the probability that a bucket is empty?"

- All the balls have the same probability: Prob.to have a ball anywhere?pr(1 ball)=48/96=0.5
- Probability to have an empty bucket:

Prob.of empty bucket?pr(EmptyBucket)
Prob.of having any ball in the bucketbucket?pr(BusyBucket)

pr(EmptyBucket)=1-pr(BusyBucket)
pr(BusyBucket)=pr(1ball)+ pr(2ball)+..+ pr(16ball)=0.5+?0.5?^2+?+?0.5?^16
pr(BusyBucket)=(0.5-?0.5?^17)/(1-0.5)=0.99
pr(EmptyBucket)=1.525??10?^(-5)

I think my calculations are not right because I have not taken into consideration that I only have 48 balls. The problem is that I am not sure how to take that into account during the calculations. How should I do to consider in the calculations that those 48 balls need to be allocated between all those 96 possible places (in the 6 available buckets)?

Thanks again!