If you spin the dial two times there three things that can happen:
1) Dial does not land in the region A
2) Dial lands once in the region A
3) Dial lands twice in the region A
The combined probability of these three events has to be 1.
Let's calculate probabilities of each event:
[tex]1) P=P(1,1)=\frac{2}{3}\cdot\frac{2}{3}=\frac{4}{9}\\
2)P=P(1,2)+P(2,1)=2\cdot \frac{2}{3}\cdot \frac{1}{3}=\frac{4}{9}\\
3)P=P(3,3)=\frac{1}{3}\cdot\frac{1}{3}=\frac{1}{9}[/tex]
If we summ all those probabilities we get 1.
The answer would table C (lower left corner).
