Answer with Step-by-step explanation:
We are given that
Total number of chosen balls =3
Total number of white balls=5
Total number of red balls=8
[tex]X_i=1[/tex] for ith selected
white ball
[tex]X_i=0[/tex] for ith red ball
a.[tex]P(X_1=1,X_2=1)=\frac{5}{13}\cdot\frac{4}{12}=\frac{5}{39}[/tex]
[tex]P(X_1=1,X_2=1)=\frac{5}{39}[/tex]
[tex]P(X_1=1,X_2=0)=\frac{5}{13}\cdot \frac{8}{12}=\frac{10}{39}[/tex]
[tex]P(X_1=1,X_2=0)=\frac{10}{39}[/tex]
[tex]P(X_1=0,X_2=1)=\frac{8}{13}\times \frac{5}{12}=\frac{10}{39}[/tex]
[tex]P(X_1=0,X_2=1)=\frac{10}{39}[/tex]
[tex]P(X_1=0,X_2=0)=\frac{8}{13}\times \frac{7}{12}=\frac{14}{39}[/tex]
[tex]P(X_1=0,X_2=0)=\frac{14}{39}[/tex]
b.[tex]P(X_1=1,X_2=1,X_3=1)=\frac{5}{13}\times \frac{4}{12}\times \frac{3}{11}[/tex]
[tex]P(X_1=1,X_2=1,X_3=1)=\frac{5}{143}[/tex]
[tex]P(X_1=0,X_2=1,X_3=1)=\frac{8}{13}\times \frac{5}{12}\times \frac{4}{11}[/tex]
[tex]P(X_1=0,X_2=1,X_3=1)=\frac{40}{429}[/tex]
[tex]P(X_1=1,X_2=0,X_3=1)=\frac{5}{13}\times \frac{8}{12}\times \frac{4}{11}[/tex]
[tex]P(X_1=1,X_2=0,X_3=1)=\frac{40}{429}[/tex]
[tex]P(X_1=1,X_2=1,X_3=0)=\frac{5}{13}\times \frac{4}{12}\times \frac{8}{11}[/tex]
[tex]P(X_1=1,X_2=1,X_3=0=\frac{40}{429}[/tex]
[tex]P(X_1=0,X_2=0,X_3=1)=\frac{8}{13}\times \frac{7}{12}\times \frac{5}{11}[/tex]
[tex]P(X_1=0,X_2=0,X_3=1)=\frac{70}{429}[/tex]
[tex]P(X_1=0,X_2=1,X_3=0)=\frac{8}{13}\times \frac{5}{12}\times \frac{7}{11}[/tex]
[tex]P(X_1=0,X_2=1,X_3=0)=\frac{70}{429}[/tex]
[tex]P(X_1=0,X_2=0,X_3=0)=\frac{8}{13}\times \frac{7}{12}\times \frac{6}{11}[/tex]
[tex]P(X_1=0,X_2=0,X_3=0)=\frac{28}{143}[/tex]
[tex]P(X_1=1,X_2=0,X_3=0)=\frac{5}{13}\times \frac{8}{12}\times \frac{7}{11}[/tex]
[tex]P(X_1=1,X_2=0,X_3=0)=\frac{70}{429}[/tex]
