The question 3(1) from the image reads:

3(1): "If $P(A) = 0.5$, $P(B) = 0.6$, and $P(A \cap B) = 0.2$, find $P(A \cup B)$."

To solve this, we will use the formula for the union of two events in probability:

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

Given:

• $P(A) = 0.5$
• $P(B) = 0.6$
• $P(A \cap B) = 0.2$

Plugging in the values:

$P(A \cup B) = 0.5 + 0.6 - 0.2$

$P(A \cup B) = 1.1 - 0.2 = 0.9$

Final Answer:

The probability $P(A \cup B)$ is $0.9$.

Would you like to ask more questions or need further details on this topic? Here are some related questions you might consider:

1. What is the meaning of $P(A \cap B)$ in probability theory?
2. How do we interpret $P(A \cup B)$ in practical scenarios?
3. Can the value of $P(A \cup B)$ ever exceed 1? Why or why not?
4. How do we find $P(A^c)$, the complement of event $A$?
5. What does it mean if two events $A$ and $B$ are mutually exclusive?

Tip: When calculating probabilities involving unions and intersections, always consider the overlap (intersection) between the events to avoid overestimating the total probability.