Let's go through the problem step by step.

(a) Experimental Probability of Landing on Red

The experimental probability is calculated by dividing the number of times the red slice was landed on by the total number of spins.

From the table:

• Number of red spins = 187
• Total number of spins = 500

So, the experimental probability of landing on red is: $P(\text{Red}) = \frac{187}{500} = 0.374$ Rounded to the nearest thousandth: 0.374.

(b) Theoretical Probability of Landing on Red

To compute the theoretical probability, we need to consider the number of red slices compared to the total number of slices. The spinner has:

• 4 red slices,
• 4 yellow slices,
• 2 blue slices.

The total number of slices is $4 + 4 + 2 = 10$. The theoretical probability of landing on red is: $P(\text{Red}) = \frac{4}{10} = 0.4$ So, the theoretical probability of landing on red is 0.4.

(c) Choosing the Correct Statement

The law of large numbers states that as the number of trials (spins) increases, the experimental probability tends to get closer to the theoretical probability. Hence, the correct statement is:

• The larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability.

Would you like any further details or explanations on these concepts?

Here are 5 related questions to extend your understanding:

1. How do you calculate the experimental probability for yellow or blue slices?
2. What factors can affect experimental probability in real-world situations?
3. Why is theoretical probability always based on the assumption of fairness in the spinner?
4. How would the probabilities change if the spinner had 12 slices instead of 10?
5. What happens to the experimental probability if we increase the number of spins significantly, say to 5000?

Tip: Always compare experimental probability with theoretical probability to check for consistency in real-world experiments!