Logical Problem [15 Gold Reward]
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by I-G-D
Yo, what's up ?
I was doing this problem with two friends of mine a few days ago... I really liked it (there are few problems that I really like) and I figured out I should give it to some other people to try to solve it. 🙂
To make things more interesting, I'll put in a 10 Gold reward. The first person to solve it gets the entire reward, everybody else gets nothing...
The problem is purely logical. Even though I'm a mathematician in real life, I know that most people dislike maths... But I assure you, you don't need a good mathematical knowledge to do one half of this problem. I'm not gonna say anything about the second half. 😛
So what is the problem ?
You have one chicken egg. The chances that the chicken survives is x. X is a given number, constant, between 0 and 1 (if x is 0.7, that means that the egg has a 70% chance to survive, for example). If it survives, it will grow up, give birth to 2 eggs, then die. These two eggs also have the probability of x to survive. This goes on with one simple rule: each egg has the probability of x to survive, grow up, then give birth to 2 eggs, and logically, the probability of 1-x to die. What is the probability that the species dies out eventually ?
I don't want to just hear the answer, I want the full solution with all the steps...
Good luck to everyone. 😉
P. S. : All Subs are greatly appreciated.
Edit : Consider that all the chickens mentioned in the problem are female, and that you have enough male chicken (roosters) to fertilize all the living hens. Hence, if the females die out, the species will die out as well. The way they make the two eggs is not important, the only thing important is that they will definitely make exactly two eggs if they survive birth.
Edit : Sparkfyre offers 5 more Gold if the problem gets solved. The reward is now 15 Gold.
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PRVO JAJO ĆE DUMRE !
POJEŠĆU GA S JOŠ 4 KOMADA I GLAVICOM LUKA !
tako sam u mogućnosti
hahah 😃
Kill the chicken = problem solved! 10 gold now pls : )
What's the probability that that happens ? 😃
Ne moze da se resi zadatak ako nema zadato X jer zavisi od njega. Evo identican primer http://en.wikipedia.org/wiki/Branching_process#Example_of_extinction_problem
Pa brate, znam da zavisi od njega. 😃
Treba da se pronadje ta zavisnost. 🙂
Integral od 0 do 1 za 1-x? 50%?
1-x veze nema s resenjem.
Dali je konačno rješenje (1-x)/x ?
30% is the highest probability ad it is with the first chicken, as with every next step the probability will be lower.
So in essence it's a bit of a trick question, but the highest probability for death to the species is 30%
That's the lowest probability, if the first egg dies out right away. But, the extinction probability is more than that, if the first egg's descendants somehow die out, that's still something more than 0.
hold on you want the probability of surviving or of dying out?
Of dying out. But it's the same thing... If the probability for dying out is A, the probability for surviving is 1-A. If you know one, you know the other one as well.
yes, but they're with different direction of change, the probability of dying out it highest at the root, and the other way around the probability of survival is highest at the end of the branches.
So generation 1 will have the highest death probability and lowest survival probability and generation n+1 will have the highest survival probability and the lowest death probability.
So there is no set probability, as it changes with every generation, hence there is no limit to the generations there is no set cumulative probability, as you can have new generations to infinity.
So at the end the probability for the species to die out is highest at generation 1 with 30% chance and lowest at generation n+1 with a probability infinitely close but not equal to 0
"So at the end the probability for the species to die out is highest at generation 1 with 30% chance and lowest at generation n+1 with a probability infinitely close but not equal to 0"
That's incorrect.
What I'm asking for is the total extinction probability, no matter how many generations the system has... Generations are not important. What if the first egg survives, and one of its kids dies ? The family tree can get quite complicated, so looking at generations doesn't help. The n+1'th generation is already dead if the n'th one is. And a part of it is dead if a part of the n'th is... It's too complex. So you can't look at things like this.
I disagree, but ok, anyway if one of the two eggs of generation 2 dies, then you're back to a situation which is the same at generation 1, you can never have a higher probability for the species to die out then at generation 1 levels, no matter where the situation appears, even if after 1000 generations you're left again wit 1 chicken, the chance of the species to die out would again be 30%.
The cumulative chance would be dependent on the generations, since there is o limit and we have infinite generations it will eventually reach an infinitely small chance of dying out, as a cumulative it is the sum of all possible chances between 30% and 0% and divided by n+1 generations.
Anyway it's very hard to try and write math formulas with words 😃, but I've had a long day so meh.
I am asking you for the cumulative chance. 🙂
Either way, you have to do this problem for all X's from 0 to 1, not just 70%.
And no, it's not divided by n+1, you just keep adding it...
fried chicken 😁
I really don't see how can this be solved... you have an endless array which is non convergent... :/
There is a probability that the tree converges, and also a probability that it doesn't converge. You can calculate it, but I never said it was easy.
I'm working on it.. wait the min... to finish the download xD
I give up xD
p.s. I'm sure the solution of the problem is somewhere here
http://shodhganga.inflibnet.ac.in/bitstream/10603/1089/5/05_chapter%202.pdf
Probability = 0,3 + 0,3 ^ 2 + 0,3 ^ 2 ^ 2 + 0,3 ^ 2 ^ 3 + ..... + 0,3 ^ 2 ^ n
You have to do it for all X's, not just x=0.7. The solution is a very nice number. 😉
Not an infinite sum or anything.
Kokoška je besmrtna 😃 Svi njeni potomci će živjeti zauvijek 😃
Da, ako je x=1. 😃
Hajde sad za ostale x-eve. 😃
dobro druze.. a koj funkcija na raspredelba na verojatnosta ja koristish.... ?
mak'se bre, ludi čovječe 😃
Pa, uzimas u obzir sve nacine da umre vrsta. Moze direktno prvo jaje, moze njegovi potomci, pa njegovi, itd. Mozes cak i da gledas broj jaja i tu da muckas nesto. Mnogo stvari ima... Vidi sta je najbolje.
xaxa abe ne zajebavaj xD
Cek, a gde je tu petao? 😛 Bez petla nema jajeta! xD
Petlova ima beskonacno mnogo da mogu da j**u kokoske koliko god treba, a sva jaja daju kokoske. 😛
da ima matematicko reshenie mora da ima model na raspredelba na verojatnosta na smrtnost.... t.e. model na raspredelba na X
50%?
69%?
the species will die out with 100% propability because you need two chicken(one male and one female) to make another egg that will eventually become a chicken
You have infinitely many male chicken, who make kids with the female ones when they grow up. All the eggs are female.
"You have one chicken egg. The chances that the chicken survives is x. X is a given number, constant, between 0 and 1 (if x is 0.7, that means that the egg has a 70% chance to survive, for example). If it survives, it will grow up, give birth to 2 eggs, then die. These two eggs also have the probability of x to survive. This goes on with one simple rule: each egg has the probability of x to survive, grow up, then give birth to 2 eggs, and logically, the probability of 1-x to die. What is the probability that the species dies out eventually ?"
- it's 0% man! Even If u have one chicken in the beginning, u cannot breed another fertilized egg with just one chicken
Imagine that you have "enough" male chicken to fertilize all the eggs in the problem.
So the chance of survive is 100%, if we always have male chicken, we ALWAYS ll have chicken... 😛
The male chicken die out if there are no females...
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@Dal2,@ELGRECO Haven't you heard the news?
Saudi Arabia has bred new brand of chickens that reproduces via parthenogenesis. Male have become obsolete : X
1-X = X-1
Well, my thought is that the highest chance for the species to die is 30% (because of the first egg) and then in each generation that percentage is getting lowered.