Q. A rod of length 10 cm is broken into three parts, so that each part is having a length as an integral multiple of 1 cm,. The probability that the parts are forming a triangle, is
A) $1/4$
B) $1/2$
C) 3/4
D) 1/3
Explanation
(a)
Let $x,y\ and\mathcal{\ z}$ be the parts and $x \leq y \leq \mathcal{z}$. Then, $\left( x,y,\mathcal{z} \right) \in (1,\ 1,\ 8),\ (1,\ 2,\ 7),\ (1,\ 3,\ 6),\ (1,\ 4,\ 5),\ (2,\ 2,\ 6),\ (2,\ 3,\ 5),\ (3,\ 3,\ 4)(2,\ 4,\ 4)\}$.Only the cases when $(x,y,\mathcal{z)}$ formed a triangle are $\{(3,\ 3,\ 4),\ (2,\ 4,\ 4)\}$,
Required probability $= \frac{2}{8} = \frac{1}{4}$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.