Math Is Fun Forum

MajikWaffle

Member

Registered: 2005-12-14

Posts: 11

Just Checking

If a 1-meter stick is cut into two independent random places, what are the odds that the pieces can for a triangle

So that's the problem right. I ran about 5 million trials with a self made program and got a probability of .25

Is that correct, and how can you algebraically prove it?

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Just Checking

The first thing to do is to come up with the requirements for the pieces to be able to form a triangle, and since you've written a program testing it, I'll assume you already have this.

Next, you need a method of cutting such that once the cuts are done, you know the exact length of each piece.  Doing this typically starts out, "Without a loss of generality".

Finally, you need to be able to count the number of times that this cut is valid or invalid.  Typically, you will get variables out of step 2 (the cutting method), and in this step you place the restriction in step 1 upon these variables.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Just Checking

Here's my reasoning, hidden in case you want to use Ricky's tips and work it out by yourself:

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Why did the vector cross the road?
It wanted to be normal.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Just Checking

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igloo myrtilles fourmis

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Just Checking

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Why did the vector cross the road?
It wanted to be normal.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Just Checking

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igloo myrtilles fourmis