Question

modeling a weather forecast
the weather forecast for next season calls for a 10% chance of wind with no rain or clouds, a 20% chance of rain with no wind, a 30% chance of clouds with no wind or rain, and a 40% chance of only sunshine. describe a 10 - section spinner that could be used to model this situation. which forecast is most likely?

Explanation:

Step1: Understand the probabilities

We have four weather events with their probabilities: wind (10%), rain (20%), clouds (30%), and sunshine (40%). We need to model this with a 10 - section spinner, so we first convert the probabilities to the number of sections they would occupy.

To find the number of sections for each event, we multiply the probability (in decimal form) by 10.

For wind: Probability = 10% = 0.1. Number of sections = \(0.1\times10 = 1\)

For rain: Probability = 20% = 0.2. Number of sections = \(0.2\times10=2\)

For clouds: Probability = 30% = 0.3. Number of sections = \(0.3\times10 = 3\)

For sunshine: Probability = 40% = 0.4. Number of sections = \(0.4\times10=4\)

Step2: Describe the spinner

We can divide the 10 - section spinner as follows:

• Color 1 section (out of 10) to represent wind (no rain or clouds).
• Color 2 sections to represent rain (no wind).
• Color 3 sections to represent clouds (no wind or rain).
• Color 4 sections to represent only sunshine.

Step3: Determine the most likely forecast

To find the most likely forecast, we compare the number of sections (or the probabilities) of each event. The event with the highest number of sections (or highest probability) is the most likely.

We have:

• Wind: 1 section (10% chance)
• Rain: 2 sections (20% chance)
• Clouds: 3 sections (30% chance)
• Sunshine: 4 sections (40% chance)

Since 4 (or 40%) is the highest among 1, 2, 3, 4, the most likely forecast is only sunshine.

Answer:

To model the situation with a 10 - section spinner: color 1 section for wind (no rain or clouds), 2 sections for rain (no wind), 3 sections for clouds (no wind or rain), and 4 sections for only sunshine. The most likely forecast is only sunshine.