Combinations and probability distributions

  • Thread starter SavvyAA3
  • Start date
  • #1
23
0

Main Question or Discussion Point

Can someone please help with the method of how to solve this problem.....

Question:
Three balls are thrown at random into 5 bowls so that each ball has the same chance of going into any bowl independently of wherever the other 2 balls fall. Determine the probability distribution of the numberof empty bowls.


The anwers are below, but i don't understand them. Can it be looked at as a success failure type poblem. with probability of success being that a bowl gets 1 ball: probability = 1/5, and the probability of a failure; 1-1/5 = 4/5. If so how do I use this to obtain the distribution.

Also can someone please tell me why in this scenario we don't look at the possibility of the ball missing the bowl - because i feel that this should be a possibility in this scenario, which then gives 6 equally likely outcomes, which would mean probabitlity of a success is then 1/6?

The anwer to this question (which I don't understand) is:
if we let R = no. of empty bowls

the distribution of R:
P(R=2) = 0.48, p(R=3) = 0.48, p(R=4) = 0.04

Please help!
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
249
Hi SavvyAA3! :smile:
Can it be looked at as a success failure type poblem. with probability of success being that a bowl gets 1 ball: probability = 1/5, and the probability of a failure; 1-1/5 = 4/5.
Yes, that's right! :smile:
If so how do I use this to obtain the distribution.

P(R=2) = 0.48, p(R=3) = 0.48, p(R=4) = 0.04
Well, try p(R=4) first … that's the probability that the second and third balls go into the same bowl as the first one … which is … ? :smile:
Also can someone please tell me why in this scenario we don't look at the possibility of the ball missing the bowl - because i feel that this should be a possibility in this scenario, which then gives 6 equally likely outcomes, which would mean probabitlity of a success is then 1/6?
erm … REALITY CHECK … ! :rolleyes:

When you're sitting in the examination room, THE ONLY REALITY IS WHAT'S ON THE QUESTION PAPER … anything else is just a mirage brought about by heat and lack of water and sleep. :wink:
 
  • #3
23
0
why reality check? The question did not state that this is not a possibility - please tell me why I can't assume this?

Thanks.
 
  • #4
360
21
The question also didn't state that aliens would not grab the balls with a tractor beam or that your dog would not eat them... do you see?
 
  • #5
tiny-tim
Science Advisor
Homework Helper
25,832
249
Hi montoyas7940! :smile:
The question also didn't state that aliens would not grab the balls with a tractor beam
hmm …
:smile: … is that what happened to you … ? :smile:
 
  • #6
360
21
Hi yourself TT!

No, fortunately aliens didn't grab my balls. :approve:

But I read about this guy once...
 

Related Threads for: Combinations and probability distributions

Replies
7
Views
3K
Replies
5
Views
2K
  • Last Post
Replies
6
Views
5K
Replies
4
Views
4K
  • Last Post
Replies
5
Views
11K
Replies
7
Views
1K
Replies
2
Views
2K
  • Last Post
Replies
4
Views
3K
Top