Math Brainteaser: Probability of Longer Piece Length

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In summary, the problem deals with finding the probability that when a piece of string is randomly cut, the longer piece is at least x times longer than the shorter piece. This can be solved by considering a continuous probability distribution and finding the ratio of lengths of favorable outcomes over the total length. It is important to note that this problem is not dealing with discrete probabilities, as there are infinite points to choose from rather than a set of finite points.
  • #1
oceanflavored
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Homework Statement


A piece of string is cut into two pieces at a randomly selected point. What is the probability that the longer piece is at least x times as long as the shorter piece?

Homework Equations


none

The Attempt at a Solution


everyone in my family tried, but we couldn't figure it out.
this problem is strange, because usually probability deals with picking something out of a sum total.

thanks for any help :biggrin:
 
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  • #2
Your family trying doesn't count so much as you trying. What did you try? Try a simple case first. What's the probability you cut the string in such a way that one piece is at least twice the length of the other? What's the measure of places where you can cut the string so it works versus the total measure of places on the string?
 
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  • #3
oceanflavored said:
usually probability deals with picking something out of a sum total.

That is the case when we deal with Discrete Probability distribution. In this case, as you can see, there are infinite points to chose from, there isn't a set of finite points that are favorable. Rather, there is a 'range' of lengths that is favorable. As such, you are dealing with a Continuous Probability distribution.

and as Dick said already, we can't help you further unless you show us something.
 
  • #4
Continuous versus discrete really aren't that different. And rohanprabhu is absolutely correct. The probability is the ratio of the length of the segments of points that work over the length of the whole segment. I sort of regret using the word 'measure' instead of 'length'. But it's really the same thing as taking the ratio of counts.
 

What is the "Math Brainteaser: Probability of Longer Piece Length"?

The "Math Brainteaser: Probability of Longer Piece Length" is a mathematical problem that involves calculating the probability of getting a longer piece length when cutting a random piece from a given length of material.

What is the purpose of this brainteaser?

The purpose of this brainteaser is to challenge individuals' understanding of probability and their ability to apply it to real-life scenarios.

How do you solve this brainteaser?

To solve this brainteaser, you need to determine the total number of possible outcomes and the number of favorable outcomes. Then, divide the number of favorable outcomes by the total number of possible outcomes to get the probability of getting a longer piece length.

What factors affect the probability of getting a longer piece length?

The factors that affect the probability of getting a longer piece length include the length of the material, the method of cutting, and the size of the random piece being cut.

Is this brainteaser applicable to real-life situations?

Yes, this brainteaser is applicable to real-life situations, particularly in manufacturing and construction industries where materials are cut to specific lengths.

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