Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 136

I don't know the branch of maths that deals with this problem

Wyatt wants to work out an estimate for the total number of wild ponies in a forest

In July, Wyatt catches 42 ponies in the forest
He puts a tag on each of these ponies and releases them

In August, Wyatt catches 60 ponies in the forest
He finds that 5 of the 60 ponies are tagged

Work out an estimate for the total number of ponies in the forest

My question; Which branch of maths is this?
Also, can you give me a clue as to where to start regards solving this. Just a hint please, not a full explanation.

I'm struggling to even guess at this one. I did think, '60 ponies, 5 of which are tagged, so, 5/60 tagged, which is 1/12
1/12 of the 60 tagged...
How does this relate to the initial number of 42 caught and tagged, then released..?
Of the intial 42 caught, 100% were tagged...
Why did he only catch 42 in July, but caught 60 in August?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,172

Re: I don't know the branch of maths that deals with this problem

I think this is an application of probability theory.

Say there are N ponies.

He tags 42, so the probability of getting a tagged one if you pick one at random is 42/N

Later you find 5 are tagged out of 60 so assume that gives the correct experimental probability value (5/60) and equate that with 42/N so giving an equation for N.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 136

Re: I don't know the branch of maths that deals with this problem

Thanks, Bob.

So 1/12 = 42/N

1*42 = 42
12*42 = N

N=504?

Check;

504 ponies. Catch, tag and release 42.

Now 42/504, or 1/12, are tagged.

Catch 60 expecting 1/12 to be tagged.

5 are tagged which is what you would expect, on average?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,172

Re: I don't know the branch of maths that deals with this problem

That's it. Just remember it's an estimate.  There is a statistical test that can be used to say how good an estimate it is, but I cannot remember it at the moment.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob