The probability that it rains on Saturday is 0.3 and the probability of raining on a Sunday is 0.4. What is the probability that it will not rain on either a Saturday or Sunday?
What type of problem is it? Fluency, understanding, reasoning or problem solving.


To determine the probability that it will **not** rain on either Saturday or Sunday, we can approach this by first finding the probability of rain on either day and then using that result.

Let:
- \( P(\text{rain on Saturday}) = 0.3 \)
- \( P(\text{rain on Sunday}) = 0.4 \)

Assuming the events are independent (rain on Saturday does not affect rain on Sunday), we use the following steps:

### Step-by-Step Solution

1. **Calculate the probability that it rains on either Saturday or Sunday:**
   - The probability of rain on either day is given by:
     \[
     P(\text{rain on Saturday or Sunday}) = P(\text{rain on Saturday}) + P(\text{rain on Sunday}) - P(\text{rain on both days})
     \]
   - Since the events are independent, the probability of rain on both days is:
     \[
     P(\text{rain on both days}) = P(\text{rain on Saturday}) \times P(\text{rain on Sunday}) = 0.3 \times 0.4 = 0.12
     \]
   - Therefore:
     \[
     P(\text{rain on Saturday or Sunday}) = 0.3 + 0.4 - 0.12 = 0.58
     \]

2. **Find the probability that it does not rain on either day:**
   - The probability of no rain on either day is the complement of the probability of rain on either day:
     \[
     P(\text{no rain on Saturday or Sunday}) = 1 - P(\text{rain on Saturday or Sunday})
     \]
     \[
     P(\text{no rain on Saturday or Sunday}) = 1 - 0.58 = 0.42
     \]

So, the probability that it will **not rain on either Saturday or Sunday is 0.42**.

### Type of Problem
This problem falls under **reasoning**. It requires an understanding of probability, specifically the rules for combining probabilities of independent events and using complements.

Would you like further explanation, or do you have any questions?

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**Related Questions:**

1. What is the probability that it will rain on both Saturday and Sunday?
2. How would the answer change if the rain events were not independent?
3. What is the probability that it rains on Saturday but not on Sunday?
4. How can we verify if two events are independent?
5. What if the probability of rain on both days together was given? How would that affect calculations?

**Tip:** When finding the probability of "not" occurring events, consider using complements, as it often simplifies calculations.

The probability that it rains on Saturday is 0.3 and the probability of raining on a Sunday is 0.4. What is the probability that it will not rain on either a Saturday or Sunday?

Calculate the probability of no rain on both Saturday and Sunday given independent rain probabilities of 0.3 and 0.4. This solution explains using the complement rule and the formula for independent events. Ideal for high school students in Grades 10-12.

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