D; D; B
Step-by-step explanation:
Question 1:
All of the outcomes are not equally likely because there is a lot of variation between the relative frequencies of the different landing positions.
As we can see from the data, the cup will most likely land sideways, then backwards, then upright. Since there is a lot of variation between the number of times this happens, we know this isn't just because of the random factor, but because there is a higher probability of it landing on its side. Additionally, the huge differences between the numbers tell us that the 3 outcomes are not equally likely. That removes option A and B. We know it isn't option C because the relative frequency of it landing sideways is not the lowest, but the highest. (Upwards: 9/60= 0.15= 15%, Upside down: 15/60= 0.25= 25%, Sideways: 36/60= 0.6= 60%) Therefore, option D is the correct answer.
Question 2:
Yes, it is a fair model because the relative frequencies of all the outcomes are similar.
We can look at the table, and understand the the relative frequencies of these outcomes will all be similar.
We can calculate it to make sure.
L: 10/40= 0.25= 25%
E: 11/40= 0.275= 27.5%
A: 9/40= 0.225= 22.5%
P: 10/40= 0.25= 25%
As you can see, the relative frequency of all these options is similar, indicating that this is a fair model.
Question 3:
Yes, it is a fair model because the relative frequencies of all the outcomes are similar.
Once again, when looking at the tables, we see that all outcomes occur a similar number of times, meaning that the model is most likely fair.
To make sure, we can calculate the relative frequencies.
Green: 12/50= 0.24= 24%
Pink: 9/50= 0.18= 18%
Yellow: 11/50= 0.22= 22%
Blue: 10/50= 0.2= 20%
Red: 8/50= 0.16= 16%
Although these frequencies aren't as similar as the previous model, I would still deem them similar enough for the model to be considered fair.
