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Let's solve the problem step by step based on the probability tree diagram.

### Problem Recap:
You need to find the probability (as a percentage) that it will rain on only one of the two days (Saturday or Sunday) over the weekend.

### Given Probabilities:
From the tree diagram:
- Probability of rain on Saturday (S): \( P(R_{\text{Sat}}) = 40\% = \frac{40}{100} \)
- Probability of no rain on Saturday: \( P(\text{No Rain}_{\text{Sat}}) = 60\% = \frac{60}{100} \)
- Probability of rain on Sunday given it rains on Saturday: \( P(R_{\text{Sun}} | R_{\text{Sat}}) = 30\% = \frac{30}{100} \)
- Probability of no rain on Sunday given it rains on Saturday: \( P(\text{No Rain}_{\text{Sun}} | R_{\text{Sat}}) = 70\% = \frac{70}{100} \)
- Probability of rain on Sunday given no rain on Saturday: \( P(R_{\text{Sun}} | \text{No Rain}_{\text{Sat}}) = 30\% = \frac{30}{100} \)
- Probability of no rain on Sunday given no rain on Saturday: \( P(\text{No Rain}_{\text{Sun}} | \text{No Rain}_{\text{Sat}}) = 70\% = \frac{70}{100} \)

### Required:
You are asked to find the probability that it will rain on only one of the two days (either Saturday or Sunday, but not both).

### Step-by-Step Solution:

To find the probability of rain on only one of the days, we need to consider two cases:
1. **Rain on Saturday and no rain on Sunday**:  
   \[
   P(\text{Rain on Saturday and No Rain on Sunday}) = P(R_{\text{Sat}}) \times P(\text{No Rain}_{\text{Sun}} | R_{\text{Sat}})
   \]
   \[
   = \frac{40}{100} \times \frac{70}{100} = \frac{2800}{10000} = 0.28 \, \text{or} \, 28\%
   \]

2. **No rain on Saturday and rain on Sunday**:  
   \[
   P(\text{No Rain on Saturday and Rain on Sunday}) = P(\text{No Rain}_{\text{Sat}}) \times P(R_{\text{Sun}} | \text{No Rain}_{\text{Sat}})
   \]
   \[
   = \frac{60}{100} \times \frac{30}{100} = \frac{1800}{10000} = 0.18 \, \text{or} \, 18\%
   \]

### Final Probability:
The total probability that it will rain on only one day is the sum of the probabilities of the two cases:
\[
P(\text{Rain on only one day}) = 28\% + 18\% = 46\%
\]

### Conclusion:
The probability that it will rain on only one of the days over the weekend is **46%**.

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Would you like any further details or have any questions? Here are five related questions to consider:

1. What is the probability that it will rain on both Saturday and Sunday?
2. How would you calculate the probability that it will not rain on either day?
3. Can this probability tree be extended for three consecutive days?
4. How do conditional probabilities affect real-life weather predictions?
5. How does the sum of probabilities for all possible outcomes relate to certainty?

**Tip:** In probability trees, always ensure that the branches for any event sum up to 1 or 100%, as this helps check the accuracy of conditional probabilities.

Complete the probability tree diagram and determine the probability (as a percentage) that it will rain on only one of the days over the weekend.

Solve the probability problem of determining the chances that it will rain on only one of the two days over the weekend using a probability tree diagram. Explore key probability concepts such as conditional probability and the law of total probability.

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