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 is sunny all three​ days?

The problem states that for each day, the weather can either be sunny or rainy, with each outcome being equally likely. This means that the probability of a sunny day is \( \frac{1}{2} \), and the probability of a rainy day is also \( \frac{1}{2} \).

To find the probability that it is sunny on all three days, we need to calculate the joint probability of sunny weather on each of the three days. Since the days are independent, we can multiply the probabilities for each day:

\[
P(\text{Sunny all three days}) = P(\text{Sunny on Day 1}) \times P(\text{Sunny on Day 2}) \times P(\text{Sunny on Day 3})
\]

\[
P(\text{Sunny all three days}) = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}
\]

So, the probability that it is sunny all three days is \( \frac{1}{8} \), or 0.125.

Would you like more details or have any questions?

Here are some related questions to think about:
1. What is the probability that it rains on all three days?
2. What is the probability that it rains on exactly two days?
3. What is the probability that it is sunny on at least one day during the trip?
4. What is the probability that it rains on the first day and is sunny on the other two days?
5. How would the probabilities change if the chance of rain was not equal to the chance of sunshine?

**Tip:** In probability, when events are independent, their joint probability can be calculated by multiplying the probabilities of each individual event.

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 is sunny all three days?

Explore how to calculate the probability of having sunny weather for three consecutive days in Seattle. This problem uses the concept of independent events in probability, applying the multiplication rule. Suitable for middle school students in Grades 6-8.

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