Combinations and probability distributions

Click For Summary

Discussion Overview

The discussion revolves around a probability problem involving the distribution of empty bowls when three balls are thrown randomly into five bowls. Participants explore the method to determine the probability distribution of the number of empty bowls, considering various interpretations of the problem.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests modeling the problem as a success-failure scenario, where the probability of a bowl receiving a ball is 1/5, and the probability of failure is 4/5.
  • Another participant confirms the success-failure model but prompts further exploration of how to derive the distribution from it.
  • Concerns are raised about the assumption that balls cannot miss the bowls, with one participant suggesting that this should be considered, leading to a different probability outcome.
  • Responses include a humorous dismissal of the possibility of missing bowls, comparing it to unlikely scenarios such as alien interference.
  • Participants engage in light banter regarding the absurdity of considering non-stated possibilities in the problem context.

Areas of Agreement / Disagreement

Participants generally agree on the basic framework of the problem but disagree on the assumptions regarding the possibility of balls missing the bowls. The discussion remains unresolved regarding the implications of these assumptions on the probability distribution.

Contextual Notes

Participants have not reached a consensus on whether to include the possibility of balls missing the bowls, which affects the interpretation of the probability distribution. The discussion reflects differing views on the assumptions that can be made based on the problem statement.

SavvyAA3
Messages
23
Reaction score
0
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!
 
Physics news on Phys.org
Hi SavvyAA3! :smile:
SavvyAA3 said:
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:
 
why reality check? The question did not state that this is not a possibility - please tell me why I can't assume this?

Thanks.
 
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?
 
Hi montoyas7940! :smile:
montoyas7940 said:
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:​
 
Hi yourself TT!

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

But I read about this guy once...
 

Similar threads

High School Relative And Absolute Probability (Probability Of Picking A Red Ball)
  • · Replies 8 ·
Replies
8
Views
3K
Graduate Calculation of probabilities assuming correlation between events
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Ways to put n balls in m boxes such that exactly k boxes are empty?
  • · Replies 29 ·
Replies
29
Views
6K
High School Probability of hitting a target
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad "Inverse" probability distribution question
  • · Replies 9 ·
Replies
9
Views
3K
High School How to combine 2 distributions with different sample sizes?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Probability of White Ball in Box of 120 Balls: Solved!
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Write probability in terms of shape parameters of beta distribution
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad What is the probability that the product of the digits is odd?
  • · Replies 13 ·
Replies
13
Views
3K
MHB Game Night : Number of combinations
  • · Replies 14 ·
Replies
14
Views
2K