Probability

A rod is divided in 3 parts randomly. The probability that they can form a triangle.

It was a subjective(write the answer) and my tukka was correct without the options :P

but anyone please with the method.

3 Answers

wlog assume that the length of the rod is 1

a+b+c=1

chose 2 points at x, y in interval (0,1) they will divide the line in 3 parts

we want that

x+1-y>y-x
y>1-y
x<1-x

plot on the xy curve within the square 0<x<y<1

you should get the answer :)

kuch aise socha ja sakta hain.........

let the smallest cut-out length be m out of L

then by observatn m>=L/4

then let the 2nd smallest piece out of the remainin 3L/4 length be t

then again by obsvtn t>=L/4

aage ........
.
.
.
.

√ √ || {} [] () → ~ ^ x x x → → ln log lg lim lim cos sin tan cot arcsin arccos arctan

∫ ∫ ∫ ∫ ∫ ∬ ∬ ∬ ∬ ∬ ∭ ∭ ∭ ∭ ∭ ⨌ ⨌ ⨌ ⨌ ⨌

∑ ∑ ∑ ∑ ∑ ∮ ∮ ∮ ∮ ∮ ∏ ∏ ∏ ∏ ∏ ∐ ∐ ∐ ∐ ∐

+ - × ÷ ± ∓ = ∪ ∩ ≠ ∼ ≈ ∅ ∀ ∃ ∈ ∋ ∝ ≤ ≥ ≃ ≅ ≡ < > ≪ ≫ ⊂ ∉ ⊃ ⊆ ⊇ ⇒ ⇐ ⇔ ⇒ ⇐ ⇔ ⇑ ⇓ ⇕ → ← ↔ → ← ↔ ↑ ↓ ↕ ↖ ↗ ↘ ↙ ↪ ↩ ⇀ ↼ ⇁ ↽

° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω