Split Line Segments

Http://www.jyeoo.com/math2/ques/detail/7b3043e2-5fe3-45f2-8a5e-d7705c76b443

Divide a line segment into three segments. The probability that the three segments can form three sides of a triangle is 1/4.

Set the length of a line segment to 10, and the length of the three segments to X, Y, 10-x-y,
The line segment is randomly converted into X of 3 segments, and the constraint of Y is

0 <x <10 0 <Y <10 0 <10-(x + y) <10

, As shown in the triangle, the area is S = 50,
The condition for forming a triangle is

X + Y> 10-x-y X + 10-x-y> Y Y + 10-x-y> X

,
The area S is shown in the shadow part of the corresponding area._{Shadow =}

25

2

,

Therefore, a line segment is randomly divided into three segments,
Probability p =

S shadow

S

= 1/4