Question

The tree diagram relates the weather forecast and school closings. Find the probability (as a percent) that the school is closed tomorrow if there is a
90% chance for heavy snow

Answer 1

To calculate the probability that the school is closed tomorrow given a 90% chance for heavy snow, we would need additional information from the tree diagram you're referencing. Specifically, we would need to know the probabilities of school closings given different weather conditions (e.g., heavy snow, light snow, no snow).

However, I can provide a general outline of how to compute this probability if you had the necessary information:

1. **Identify the probabilities from the tree diagram**:
- Let \( P(H) = 0.90 \) be the probability of heavy snow.
- Determine \( P(C | H) \), the probability that school is closed given heavy snow.
- You might also need to know the probabilities for other weather conditions (e.g., light snow or no snow) and their corresponding closing probabilities.

2. **Use the Law of Total Probability**:
- If you have the other weather probabilities, you can calculate the overall probability of school closing using:
\[
P(C) = P(C | H) \cdot P(H) + P(C | L) \cdot P(L) + P(C | N) \cdot P(N)
\]
where \( L \) and \( N \) represent light snow and no snow, respectively, and \( P(C | L) \) and \( P(C | N) \) are the probabilities of closing given those conditions.

3. **Convert to Percent**:
- Once you compute \( P(C) \), convert it to a percentage by multiplying by 100.

If you provide the additional probabilities related to school closings given the weather conditions, I would be happy to help you calculate the exact probability!