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A stick is 5 units long. It is broken at two points, chosen at random. What is the probability that all three pieces are longer than 1 unit?

 Dec 18, 2019
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Let the pieces be x, y and 5-(x+y)

where 

0

0

also

0<5-(x+y)<5

-5<-(x+y)<0

0

y< -x+5,     y>-x

 

Draw that up on a number plane and you get a triangle with an area of 12.5  that is your sample space.

 

Now graph the favourable area.   And work out what it is.

x>1

y>1

5-(x+y)>1

 

You can take over from here.

 Dec 18, 2019

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