Select the correct answer.
Royston and his friends toss a paper cup to see how it lands. They repeat this experiment 60 times and record the results in a table.

Landing Position	Times Result Occurred
upright	
9
upside down	
15
sideways	
36

Which statement is true based on the results in the table?

 A. 
All of the outcomes are equally likely because their relative frequencies are similar.
 B. 
All of the outcomes are equally likely because the relative frequency of being upright is similar to that of being upside down.
 C. 
All of the outcomes are not equally likely because the relative frequency of landing sideways is the lowest.
 D. 
All of the outcomes are not equally likely because there is a lot of variation between the relative frequencies of the different outcomes.

To determine which statement is true, let's first calculate the relative frequencies for each landing position:

1. **Relative frequency of landing upright:**
   \[
   \frac{9}{60} = 0.15
   \]

2. **Relative frequency of landing upside down:**
   \[
   \frac{15}{60} = 0.25
   \]

3. **Relative frequency of landing sideways:**
   \[
   \frac{36}{60} = 0.60
   \]

Based on these calculations, we can see there is a significant variation in the relative frequencies of the different outcomes. The sideways outcome has a much higher relative frequency compared to the other outcomes. 

Thus, the correct statement is:

**D. All of the outcomes are not equally likely because there is a lot of variation between the relative frequencies of the different outcomes.**

**Do you have any questions or need further details?**

Here are some additional questions you might be interested in:

1. How does the total number of trials affect the relative frequency?
2. What is the significance of a relative frequency being much higher than others?
3. How can you interpret the likelihood of an outcome based on relative frequency?
4. What additional data might you collect to understand the probability distribution better?
5. How would you determine if any bias affects the cup’s landing position?

**Tip:** When evaluating probabilities and relative frequencies, always check for significant differences to assess if outcomes are equally likely or not.

Explore the concept of probability through Royston and his friends' paper cup experiment. Analyze relative frequencies of upright, upside down, and sideways landings to determine their likelihood. Suitable for Grades 7-9 mathematics.

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