Now use the information you are given and the General Addition Rule to find the desired probability, P(smoke is detected).

To find the probability $P(\text{smoke is detected})$ using the General Addition Rule, we will first need clarity on the events involved. Typically, the General Addition Rule applies when we have two events, say $A$ and $B$, and it states:

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

Assuming $A$ represents the event that "smoke is detected" and $B$ represents another relevant event, let’s identify the necessary components to apply this rule.

1. ### Break Down the Problem

1. Identify events $A$ and $B$.
2. Gather the probabilities: $P(A)$, $P(B)$, and $P(A \cap B)$ if applicable.

2. ### Relevant Concepts

• General Addition Rule: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$

3. ### Analysis and Detail

• Substitute the values into the equation based on the information provided.
• Calculate $P(A \cup B)$ using the formula, ensuring all parts are accurately incorporated.

4. ### Verify and Summarize

• Double-check the probability values and ensure the calculation follows the addition rule correctly.

Final Answer

Once the probabilities are provided, plug in the values into the formula to compute $P(\text{smoke is detected})$. If there are no additional events or dependencies, the probability could simply be $P(A)$ if $A$ stands alone without intersection with any other event.

If you can provide specific probabilities or additional context about other intersecting events, I can give you a more precise calculation.