霧切息災(zāi)池,兩個(gè)都想要,定軌誰(shuí)?數(shù)學(xué)證明
設(shè)定息災(zāi) 最好情況直接兩個(gè)都出的概率是 霧息0.75*0.5*0.75*0.5=0.140625? 息霧同上 以下用簡(jiǎn)稱, 息常霧0.75*0.5*0.25*0.5=0.046875 息常息霧0.75*0.5*0.25*0.5=0.046875 霧霧息0.75*0.5*0.75*0.5=0.052734375? 霧常息0.75*0.5*0.25=0.09375? 常霧息0.25*0.5=0.125? 常息霧0.25*0.5*0.75*0.5=0.046875 常息息息霧0.25*0.5*0.75*0.5*0.75*0.5=0.017578125 常息息霧0.25*0.5*0.75*0.5*0.75*0.5=0.017578125 以上 無(wú)論定軌誰(shuí),都能抽到的概率是相同的,因此,不考慮抽取的具體次數(shù)(如果需要進(jìn)一步計(jì)算,也可以用金數(shù)當(dāng)權(quán)數(shù)加權(quán),求期望抽數(shù),這里我就不算了) 2*0.140625+0.046875+2*0.046875+0.0527343+0.09375+0.125+0.046875+3*0.017578125+2*0.017578125=0.828124925 2*0.140625+0.046875+2*0.052734375+0.09375+0.125+0.046875+0.017578125+0.017578125=0.734375 計(jì)算得定軌息災(zāi) 抽取息災(zāi)的期望為0.828124925 霧切期望為0.734375 結(jié)論為:更能接受兩把霧切的傾向于定軌霧切 更能接受兩把息災(zāi)的(?,我也不知道為什么)傾向于定軌息災(zāi) 設(shè)為定軌霧切的結(jié)論也是一樣的,就不算了 是與定軌同向的,符合直覺(jué)和期待