You are planning a​ three-day trip to​ Seattle, Washington, in October. Use the fact that on each​ day, it could either be sunny or​ rainy, and that each day is equally likely to be sunny or rainy to answer the following question.

What is the probability that it rains on at least one​ day?




To solve this, we can use the concept of complementary probability. 

### Step-by-step:

1. The total number of possible outcomes for weather over the three days is based on two possibilities (sunny or rainy) each day. Since there are 3 days, the total number of outcomes is:
   \[
   2^3 = 8
   \]
   These outcomes are: 
   - SSS (sunny, sunny, sunny)
   - SSR, SRS, RSS, etc. (combinations of sunny and rainy)

2. Now, we calculate the probability that it rains on at least one day. It's easier to first find the probability of the opposite event, which is that it **does not rain at all** (i.e., all days are sunny). 

   - The probability that it is sunny on any given day is \( \frac{1}{2} \).
   - Therefore, the probability that it is sunny on all 3 days is:
     \[
     \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}
     \]

3. The probability that it rains on at least one day is the complement of this event:
   \[
   P(\text{at least one rainy day}) = 1 - P(\text{no rain at all})
   \]
   \[
   P(\text{at least one rainy day}) = 1 - \frac{1}{8} = \frac{7}{8}
   \]

### Final Answer:
The probability that it rains on at least one day is \( \frac{7}{8} \), or 87.5%.

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### Related Questions:
1. What is the probability that it rains on exactly one day?
2. What is the probability that it rains on all three days?
3. How would the probability change if the forecast predicted a 60% chance of rain each day?
4. What is the probability that it rains on at least two days?
5. How would you calculate the probability of specific sequences like "sunny-rainy-rainy"?

**Tip**: Using complementary probability is often easier for "at least" or "at most" problems!

You are planning a​ three-day trip to​ Seattle, Washington, in October. Use the fact that on each​ day, it could either be sunny or​ rainy, and that each day is equally likely to be sunny or rainy to answer the following question: What is the probability that it rains on at least one​ day?

Learn how to calculate the probability that it rains on at least one day during a three-day trip to Seattle in October. This problem uses the concept of complementary probability and is suitable for students in Grades 8-10. Find out the step-by-step solution for the probability of rain and related questions.

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