一道看似是生物题的概率题

题目如图所示

三代解体思路如图所示

三代中红所占比例=$0.75\times0.75\times0.75=0.75^{3}$0.75×0.75×0.75=0.753
三代中绿所占比例=$(0.75\times0.75\times0.1)+(0.75\times0.1\times0.75)+(0.25\times0.75\times0.75)=0.75^{2}\times0.1\times2+0.25\times0.75^{2}=0.75^{2}\times0.45$(0.75×0.75×0.1)+(0.75×0.1×0.75)+(0.25×0.75×0.75)=0.752×0.1×2+0.25×0.752=0.752×0.45
三代中黑所占比例=1-红-黑

同理可推
11代中红=$0.75^{11}$0.7511
11代中绿=$0.75^{10}\times0.1+0.75^{9}\times0.1\times0.75+...+0.75\times0.1\times0.75^{9}+0.25\times0.75^{10}=0.75^{10}\times0.1\times10+0.25\times0.75^{10}=0.75^{10}\times0.45$0.7510×0.1+0.759×0.1×0.75+...+0.75×0.1×0.759+0.25×0.7510=0.7510×0.1×10+0.25×0.7510=0.7510×0.45
11代中黑=1-红-绿