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:

$$ \begin{aligned} P(A \text{ and } B) &= P(A) \cdot P(B) \\ P(A \text{ and } B) &= 0.77 \cdot 0.15 \\ P(A \text{ and } B) &= 0.1155 \end{aligned}$$

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:

$$ \begin{aligned} P(A \text{ or } B) &= P(A) + P(B) - P(A \text{ and } B) \\ P(A \text{ or } B) &= 0.77 + 0.15 - 0.1155 \\ P(A \text{ or } B) &= 0.8045 \end{aligned}$$

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