Solving Probability Questions: 2 Homes, Cats, Dogs

  • Context: Undergrad 
  • Thread starter Thread starter miscellaneous_
  • Start date Start date
  • Tags Tags
    Probability
Click For Summary

Discussion Overview

The discussion revolves around a probability question involving two homes, a set number of cats and dogs, and how to calculate the likelihood of specific combinations of pets in each home. The scope includes combinatorial reasoning and probability theory.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant suggests that the problem may involve combinatorial calculations and initially considers a binomial distribution but finds it does not fit after calculations.
  • Another participant emphasizes the need for more context to answer the question, asking for known information.
  • A participant provides specific details about the total number of animals, stating there are 4 cats and 8 dogs, and discusses the probabilities of selecting each type of animal without replacement.
  • One participant proposes that if homes are twice as likely to choose a dog over a cat, the selection process might involve alternating picks until each home has three pets, suggesting that the total population of animals does not affect the probabilities for the selections of interest.
  • There is a question raised about the total number of possibilities, with a participant suggesting the use of combinations (12C4) to calculate this.

Areas of Agreement / Disagreement

Participants express differing views on how to approach the problem, with no consensus reached on the correct method or interpretation of the question. The discussion remains unresolved regarding the specifics of the probability calculations.

Contextual Notes

Participants mention various assumptions, such as the independence of picks and the order of selection not mattering, but these assumptions are not universally accepted or clarified.

miscellaneous_
Messages
2
Reaction score
0
Hey, I think this is a combinatorial question and I'm too far removed from stats to remember. I thought it was originally a binomial distribution but then that didn't make sense after I calculated it.

What is the probability of 2 homes with 2 cats and 1 dog and 2 homes with 3 dogs?

How would I solve this type of question in general. Thanks.
 
Physics news on Phys.org
Welcome to PF;
The question cannot be answered without more context.
What is the known information?
 
Thanks Simon,
There are 4 cats and 8 dogs in total.
The probability of picking a cat is simply 1/3 and the probability of picking a dog is 2/3 initially (i.e. one animal is not inherently more probable to be chosen).
There is no replacement after picking an animal.
Order does not matter.
There is nothing else that I can think of. The question could be anything, 2 teams with 2 boys and 1 girl and 2 teams with 3 girls. Basically dividing the subset of the population into specific groups.
Is there anything specific I'm not thinking about because I feel like a moron.
I hope there is a really complex answer ... it's probably not.

The total number of possibilities is 12C4 right?
 
Last edited:
OK - so houses are twice as likely to want a dog as a cat.

Guessing:
There are two homes - they take turns picking until each has three pets and each pick is independent?

If the guess is true, then:
You cannot run out of one animal for the selections of interest, so it does not matter how many dogs and cats are in the population: the probabilities won't change.

Each home with combination cat-cat-dog (any order)
What is the probability of one home picking cat-cat-dog?
 

Similar threads

  • · Replies 13 ·
Replies
13
Views
1K
  • · Replies 41 ·
2
Replies
41
Views
10K
  • · Replies 14 ·
Replies
14
Views
2K
  • · Replies 11 ·
Replies
11
Views
4K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 29 ·
Replies
29
Views
6K
  • · Replies 17 ·
Replies
17
Views
3K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K