→ TOOYA:才會形成三角形 手誤 02/10 19:33
※ 引述《peecome (bunnyplaycat)》之銘言：
: Take a stick of unit length and break it into two pieces, choosing the break
: point at random. Now break the longer of the two pieces at a random point.
: What is the probability that the three pieces can be used to form a triangle?
: 想請問大家覺得該怎麼解?
: 我令一推隨機變數越來越複雜...
: 謝謝..
x1 x1
├──┼────┼──┼────┤
0 x1 x2 x3 1
假設長度為1 第一點如果取在x1 則 第二點只能取在x2跟x3之間 常會形成三角形
算x1在左半的機率 再乘2
1/2
2*∫ 1 * x/(1-x) dx = 2log2 - 1
0
有錯請告知^^
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