概率,黑球白球

设A_i表示取出的4个球中有i个白球,i=0,1,2,3,4
B表示两代中各取一球颜色相同
P(B)=P(A_0)P(B|A_0)+P(A_1)P(B|A_1)+P(A_2)P(B|A_2)+P(A_3)P(B|A_3)+P(A_4)P(B|A_4)
=0+16/C8^4 *6/16+C4^2C4^2/C8^4*1/2+C4^3C4^1/C8^4*6/16+0
=[16/70*6/16+36/70*1/2+16/70*6/16]
=3/7
P(A_0|B)=P(A_4/B)=0
P(A_1|B)=P(A_3|B)=6/70*7/3=1/5
P(A_2|B)=18/70*7/3=18/30=6/10=3/5
家袋中有2个白球的概率最大,概率值均为3/5