Step 1:

To find $ P(A \text{ and } B) $ we use multiplication rule for independent events:

$$ \color{blue}{P(A \text{ and } B) = P(A) \cdot P(B)} $$

In this example we have:

$$ \begin{aligned} P(A \text{ and } B) &= P(A) \cdot P(B) \\ P(A \text{ and } B) &= \frac{ 1 }{ 3 } \cdot \frac{ 1 }{ 3 } \\ P(A \text{ and } B) &= \frac{ 1 }{ 9 } \end{aligned}$$

Step 2:

To find $ P(A \text{ or } B) $ we use an addition rule:

$$ \color{blue}{P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)}$$

In this example we have:

$$ \begin{aligned} P(A \text{ or } B) &= P(A) + P(B) - P(A \text{ and } B) \\ P(A \text{ or } B) &= \frac{ 1 }{ 3 } + \frac{ 1 }{ 3 } - \frac{ 1 }{ 9 } \\ P(A \text{ or } B) &= \frac{ 5 }{ 9 } \end{aligned}$$

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