Answer
$\dfrac{1}{3}$
Work Step by Step
The experiment involves spinning $\text{Spinner III}$ followed by $\text{Spinner II}$.
Thus, the sample space $S$ is:
$S=\left\{\text{Forward Yellow}, \text{Forward Green}, \text{Forward Red},
\text{Backward Yellow}, \\
\space \space \space \space \space \space \space \space \space\text{Backward Green}, \text{Backward Red}\right\}$
Note that $n(S)=6$ and that each one has an equal chance of happening (equally-likely outcomes).
Let $E_1$ be the event that the outcome is Forward followed by a Green.
Then, from the sample space, we have $P(E_1)=\dfrac{1}{6}$.
Let $E_2$ be the event that the outcome is Forward followed by a Yellow.
Then, $P(E_2)=\dfrac{1}{6}$.
Let $E$ = event that a Forward comes out followed by a Green or a Yellow.
Then,
$P(E)=P(E_1)+P(E_2)=\dfrac{1}{6}+\dfrac{1}{6}=\dfrac{2}{6}=\dfrac{1}{3}$
