Bayesian probability of this problem

In summary: This is a forum for discussing problems and solutions, not just for obtaining them. In summary, the problem involves two breeding strategies for fictional Furble creatures: Dominator Furbles who fight for breeding territory and can rear 10 offspring if they win, and Sharers who share territory with another Furble and can rear 5 offspring. Sharers who attempt to share with dominators are forced out of the territory but can find a new one and produce 3 offspring due to lost time. Dominators always force sharers out and rear 10 young, but when they meet other dominators they win 50% of the time and are unable to reproduce due to injuries when they lose. With a population of 2000 dominator and shar
  • #1
datatec
17
0
This problem I took from an IQ test I found:

Consider two breeding strategies of the fictional Furble. Dominator Furbles can fight for a breeding territory, and if they win, will be able to rear 10 offspring. An alternative is to share territory with another Furble which will allow each to rear 5 offspring. Sharers who attempt to share with dominators will be forced out of the territory, although they will be able to find a new territory. Assume sharers become extra cautious after encountering a dominator and so will always find another territory to share the next time around, but due to lost time will only be able to produce 3 offspring. Dominators are always able to force sharers out of the territory and rear 10 young. Dominators who meet dominators will win 50% of the time. When they lose, they are not able to reproduce that season due to sustained injuries. Individual Furbles cannot switch strategies.

With a total population of 2000 dominator and sharer Furbles, how many would you expect to be dominators?


The extraordinary difficulty of this problem lies in the number of combinations the the dominators and shares can make. One thing is clear, in order to solve this problem we need to maximize the amount of offspring the community can have. I can see a lot of complexity around the bayesian probability of this problem. Can anyone help me solve it?¿
 
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  • #2
the problem is not well posed because it leaves out key information. for example are the offspring of a D-type always D-type. Is the type hereditary? To solve the problem doesn't one have to make this (and other) clarifying assumptions?

the problem says, about S-type, "although they will be able to find a new territory"
THAT SUGGESTS THAT THERE IS INFINITE AMOUNT OF TERRITORY AVAILABLE!

so there is no bound on population growth, in this picture. at least the S-type is always able to find more territory and reproduce either 3 or 5 offspring. So the population will not stabilize but will grow exponentially.

the problem does not say that the D-type is assured of finding territory.
this is very strange. perhaps the D-type and S-type require different kinds of territory and there is only a finite amount of the kind needed by the D-type.

if they use the same kind of territory and are both able to find it, then the D-type population would also grow exponentially without bound.

this problem becomes a game of inventing extra assumptions to make it meaningful, so you can solve it. what extra assumptions would you like to add?


Consider two breeding strategies of the fictional Furble. Dominator Furbles can fight for a breeding territory, and if they win, will be able to rear 10 offspring. An alternative is to share territory with another Furble which will allow each to rear 5 offspring. Sharers who attempt to share with dominators will be forced out of the territory, although they will be able to find a new territory. Assume sharers become extra cautious after encountering a dominator and so will always find another territory to share the next time around, but due to lost time will only be able to produce 3 offspring. Dominators are always able to force sharers out of the territory and rear 10 young. Dominators who meet dominators will win 50% of the time. When they lose, they are not able to reproduce that season due to sustained injuries. Individual Furbles cannot switch strategies.

With a total population of 2000 dominator and sharer Furbles, how many would you expect to be dominators?


The extraordinary difficulty of this problem lies in the number of combinations the the dominators and shares can make. One thing is clear, in order to solve this problem we need to maximize the amount of offspring the community can have. I can see a lot of complexity around the bayesian probability of this problem. Can anyone help me solve it?
 
  • #3
I do agree that assumptions need to be made however these assupmtions are by no means subjective. They will be the same for all people using rational logic to solve this problem. I believe that we need to maximize the offspring the community of furbles can have. I believe that we only need to take into consideration the first generation (only one process of reproduction) and so the offspring of a particular type of furble is irrelevant. Furthurmore I battle to see what territoy has to do with the problem as it is simple a case of combining S-types and D-types with no consideration of territoy size.

The above remarks are all my own opinion and I admit I may be wrong. In order to solve the problem would we have to take into consideration the next generation of Furbles? My guess is we would not need to as the problem does not specify as to wether the offspring are of the same type.

More thoughts on this problem are welcome...
 
  • #4
Why do you think you must maximize the offspring?
 
  • #5
No other parametres are posed and thus we must say that the only objective of the community is to breed.
 
  • #6
How do we tell if dominators are on the same territory? The problem is impossible unless we make assumptions.
 
  • #7
this is not exactly math puzzle. it's more like english problem. I u don't get conditions u cannt find right answer. and I'm not good with engl.

If anybody interested and HAVE TIME will be glad to cooperate. :smile:
 
  • #8
That question is from an IQ test at http://www.highiqsociety.com and they've asked that the questions and answers from the test not be shared over forums. All I can say, is that all the needed information is given in the problem.
 
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  • #9
Rahmuss obviousely solved it. ;-)

I have no intention of disrupting integrity of test. To be clear.
 
Last edited:
  • #10
I have solved the furble question as well. Quite hard.
 

Related to Bayesian probability of this problem

What is Bayesian probability?

Bayesian probability is a statistical method for calculating the likelihood of an event occurring based on prior knowledge or assumptions. It uses Bayes' theorem to update the probability of an event as new evidence or information is obtained.

How is Bayesian probability different from traditional probability?

Traditional probability is based on the frequency of an event occurring in a large number of trials, while Bayesian probability incorporates prior knowledge and adjusts the probability based on new evidence. Traditional probability is also based on the concept of "randomness," while Bayesian probability takes into account the uncertainty and variability of real-world situations.

How is Bayesian probability used in science?

Bayesian probability is widely used in science for various purposes, such as data analysis, hypothesis testing, and predictive modeling. It is particularly useful in situations where there is limited data or complex relationships between variables, and it allows for the incorporation of prior knowledge and assumptions into the analysis.

What are the advantages of using Bayesian probability?

One of the main advantages of Bayesian probability is its flexibility and ability to incorporate prior knowledge and assumptions into the analysis. It also allows for the continuous updating of probabilities as new evidence is obtained, making it useful for decision-making and prediction. Additionally, Bayesian probability can handle complex and non-linear relationships between variables, making it applicable to a wide range of problems.

What are the limitations of Bayesian probability?

One limitation of Bayesian probability is that it heavily relies on the choice of prior probabilities and assumptions, which can introduce bias into the analysis. It also requires a sufficient amount of data to accurately estimate the probabilities. Additionally, Bayesian probability can be computationally intensive and may not be suitable for large datasets.

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