A stick is broken at two points, at random. If the length of the stick is 6, then what is the probability that all three resulting pieces are shorter than 3 units?
+118680 A stick is broken at two points, at random. If the length of the stick is 6, then what is the probability that all three resulting pieces are shorter than 3 units?
I'd use contour probability mapping
Let one piece be x another y-x and the third 6-y
we know
0
y-x>0 which simplifies to y>x
y-x<6 which simplifies to y
and
0<6-y<6 which simplifies to -6<-y< 0 or better still 0
Plot all those lines on a number plane.
The area in the middle conatins all the possible outcomes.
Now you want the section inside where
x<3
y-x<3 and
6-y<3
Find the area contained in this smaller region
Put the little area over the big area and you have your probability.
