Solving Probability Questions: 2 Homes, Cats, Dogs

[miscellaneous_]

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 probabilty 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.

 

[Simon Bridge]

Welcome to PF;
The question cannot be answered without more context.
What is the known information?

 

[miscellaneous_]

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?

 

[Simon Bridge]

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?

 

[blue_raver22]

I would approach this question by first clarifying the assumptions and parameters involved. For example, are we assuming that the homes are randomly selected or are they specific homes with known pet ownership? Are we considering all possible combinations of pets or only those that meet the given criteria?

Once these details are established, we can use principles of combinatorics and probability to solve the question. In this case, we can use the formula for calculating the probability of a specific combination of events (in this case, 2 homes with 2 cats and 1 dog and 2 homes with 3 dogs) out of all possible combinations.

In general, solving probability questions involves identifying the relevant variables, determining the probability distribution, and then using mathematical tools such as combinatorics, binomial distribution, or other statistical methods to calculate the desired probability. It is also important to keep in mind any assumptions or limitations in the problem and to carefully interpret the results in the context of the problem.