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# help is appreciated, thank you

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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.

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