Example:Buffon's Needle So the probability of intersection is p《m- x(x,)dxde 4 sin 0 二 πd xde= -月 21 21Example: Buffon’s Needle ◼ So the probability of intersection is 𝑃 𝑋 ≤ 𝑙 2 sin 𝜗 = ඵ 𝑋≤ 𝑙 2 sin 𝜃 𝑓𝑋,𝜗 𝑥, 𝜃 𝑑𝑥𝑑𝜃 = 4 𝜋𝑑 න 0 𝜋/2 න 0 𝑙 2 sin 𝜃 𝑑𝑥𝑑𝜃 = 4 𝜋𝑑 න 0 𝜋/2 𝑙 2 sin 𝜃 𝑑𝜃 = 2𝑙 𝜋𝑑 − cos 𝜃 อ 𝜋 2 0 = 2𝑙 𝜋𝑑