A-wooden-stick-was-broken-randomly-into-three-pieces-What-is-the-probability-that-a-triangle-can-be-built-from-those-three-parts-

Question Number 12506 by Joel577 last updated on 24/Apr/17

A wooden stick was broken randomly into

three pieces . What is the probability that a triangle

can be built from those three parts ?

Answered by mrW1 last updated on 25/Apr/17

{L e t}^{'} s s a y t h e w o o d e n s t i c k i s b r o c k e n

i n t o t h r e e p i e c e s A, B, C .

T h e l e n g t h o f w o o d e n s t i c k i s 1 .

W h e n a w o o d e n s t i c k i s b r o c k e n i n t o

3 p i e c e s, t h e r e a r e 4 p o s s i b i l i t i e s :

1) n o n e o f t h e t h r e e p i e c e s i s l o n g e r

t h a n o r e q u a l t o 1 / 2;

2.1) o n e o f t h e t h r e e p i e c e s i s l o n g e r

t h a n o r e q u a l t o 1 / 2, a n d t h i s p i e c e i s A;

2.2) o n e o f t h e t h r e e p i e c e s i s l o n g e r

t h a n o r e q u a l t o 1 / 2, a n d t h i s p i e c e i s B;

2.3) o n e o f t h e t h r e e p i e c e s i s l o n g e r

t h a n o r e q u a l t o 1 / 2, a n d t h i s p i e c e i s C .

O n l y i n c a s e 1) t h e t h r e e p i e c e s c a n

b u i l d a t r i a n g l e .

\Rightarrow p r o b a b i l i t y = 1 / 4 .

Answered by ajfour last updated on 24/Apr/17

∙ b r e a k t h e s t i c k a n y w h e r e

∙ f o r s u c c e s s b r e a k t h e l a r g e r

o f t h e t w o p i e c e s

s o p r o b a b i l i t y t h a t a t r i a n g l e

i s f o r m e d = 1 \times (1 / 2) .

Commented by mrW1 last updated on 25/Apr/17

w h a t i f t h e s t i c k i s b r o k e n i n t o t w o

e q u a l p i e c e s ?

b r e a k t h e l a r g e r o f t h e t w o p i e c e s d o e s n t

a l w a y s m e a n s u c c e s s, e . g .

b r e a k 1 i n t o : 1 / 5, 4 / 5

b r e a k 4 / 5 i n t o : 1 / 5, 3 / 5

1 / 5, 1 / 5 a n d 3 / 5 c a n n o t b u i l d a t r i a n g l e .

Commented by ajfour last updated on 25/Apr/17

t h a n k s f o r t h e l i g h t .

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