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A stick has a length of 5 units. The stick is then broken at two points, chosen at random. What is the probability that all three resulting pieces are shorter than 2 units?

 Jun 16, 2021
 #1
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your question has been answered, I have attached a like below.


https://web2.0calc.com/questions/i-m-confused-about-this

 Jun 16, 2021
 #2
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The stick is 5 units long. Let the 3 pieces be x, y and 5 - (x + y)

Now this means that 

                  \( 0 ≤ x ≤ 5\)

                   \( x ≤ y \)   and 

                   \(0 ≤ y ≤ 5\)

 

This graph represents the sample space 

 

Area of sample space \(={1\over 2}× 5×5 = 12.5\) sq. units

 

Now the probability that all 3 resulting pieces are shorter than 2 units

                   \( x < 2\)

                   \(y<2\)  and 

                   \(5-(x+y)<2\)

 

Area of triangle \(={1\over 2}×\sqrt2×\sqrt5\)  \(={\sqrt{10}\over 2}\) \(=1.6\) sq. units 

 

∴ P(all 3 pieces are shorter than 2 units) \(={1.6\over 12.5} = 0.128\)

 Jun 16, 2021

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