$A=\left\{\text{bb};\text{bg};\text{gb}\right\}$

$P\left(A\right)=P\left(\text{bb}\right)+P\left(\text{bg}\right)+P\left(\text{gb}\right)=\frac{2}{6}\cdot\frac{1}{5}+\frac{2}{6}\cdot\frac{1}{5}+\frac{1}{6}\cdot\frac{2}{5}=\frac{2}{30}+\frac{2}{30}+\frac{2}{30}=\frac{6}{30}=\frac{1}{5}$

$B=\left\{\text{bb};\text{bg};\text{br};\text{gb};\text{rb}\right\}$

$P\left(B\right)=P\left(\text{bb}\right)+P\left(\text{bg}\right)+P\left(\text{br}\right)+P\left(\text{gb}\right)+P\left(\text{rb}\right)=\frac{2}{6}\cdot\frac{1}{5}+\frac{2}{6}\cdot\frac{1}{5}+\frac{2}{6}\cdot\frac{3}{5}+\frac{1}{6}\cdot\frac{2}{5}+\frac{3}{6}\cdot\frac{2}{5}=\frac{2}{30}+\frac{2}{30}+\frac{6}{30}+\frac{2}{30}+\frac{6}{30}=\frac{18}{30}=\frac{3^{ }}{5}$

$C=\left\{\text{rb};\text{rr}\right\}$

$P\left(C\right)=P\left(\text{bb}\right)+P\left(\text{rr}\right)=\frac{2}{6}\cdot\frac{1}{5}+\frac{3}{6}\cdot\frac{2}{5}=\frac{2}{30}+\frac{6}{30}=\frac{8}{30}=\frac{4}{15}$

$D=\left\{\text{bb};\text{bg};\text{gb}\right\}$

$P\left(D\right)=P\left(\text{bb}\right)+P\left(\text{bg}\right)+P\left(\text{gb}\right)=\frac{2}{6}\cdot\frac{1}{5}+\frac{2}{6}\cdot\frac{1}{5}+\frac{1}{6}\cdot\frac{2}{5}=\frac{2}{30}+\frac{2}{30}+\frac{2}{30}=\frac{6}{30}=\frac{1}{5}$



$A=\left\{bb,bg,gb,gg\right\}$

$P\left(A\right)=\frac{2}{6}\cdot\frac{2}{6}+\frac{2}{6}\cdot\frac{1}{6}+\frac{1}{6}\cdot\frac{2}{6}+\frac{1}{6}\cdot\frac{1}{6}=\frac{9}{36}=\frac{1}{4}$

$B=\left\{bb,bg,br,gb,rb\right\}$

$P\left(B\right)=\frac{2}{6}\cdot\frac{2}{6}+\frac{2}{6}\cdot\frac{1}{6}+\frac{2}{6}\cdot\frac{3}{6}+\frac{1}{6}\cdot\frac{2}{6}+\frac{3}{6}\cdot\frac{2}{6}=\frac{20}{36}=\frac{5}{9}$

$C=\left\{bb,gg,rr\right\}$

$P\left(C\right)=\frac{2}{6}\cdot\frac{2}{6}+\frac{1}{6}\cdot\frac{1}{6}+\frac{3}{6}\cdot\frac{3}{6}=\frac{14}{36}=\frac{7}{18}$

$D=\left\{bb,\ bg,gb\right\}$

$P\left(D\right)=\frac{2}{6}\cdot\frac{2}{6}+\frac{2}{6}\cdot\frac{1}{6}+\frac{1}{6}\cdot\frac{2}{6}=\frac{8}{36}=\frac{2}{9}$