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A stick is broken at two points.  If the length of the stick is 6, then what is the probability that all three resulting pieces are shorter than 3 units?

 Jan 8, 2023
 #2
avatar+118207 
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Let the 3 pieces by   x,     6 - y   and  y-x     long

Note that when you add these up you get 6

 

You know that each of these must be between 0 and 6 units long.

GRAPH the sample space.  Find Area of sample space

 

Now overlay that with the desired area where all the pieces  are less than 3 units long.  Find the area of this event

 

Probability = area of event/ area of sample space

 

This is called probability contour mapping.

 Jan 9, 2023
 #3
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Can u just give me the answer?

Guest Jan 9, 2023
 #4
avatar+118207 
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24.6    that is an answer.   (maybe not to this question though)

Melody  Jan 15, 2023
edited by Melody  Jan 15, 2023
 #5
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Honestly, you're lucky to get complete solutions at all. We're doing your work for free, and more demands aren't exactly sufficient incentives for proffering full solutions.

EquationEnthusiast  Jan 16, 2023

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