To solve the questions in the image:

(a) Theoretical Probability

The spinner has 10 equally sized slices. To find the theoretical probability of landing on black or white:

1. Count the number of black and white slices: There are 3 black and 2 white slices.
2. Total slices: 10

The theoretical probability $P(\text{Black or White})$ is: $P(\text{Black or White}) = \frac{\text{Number of Black + White Slices}}{\text{Total Slices}} = \frac{3 + 2}{10} = \frac{5}{10} = 0.5$

(b) Experimental Probability

Nicole spun the dial 40 times, with the results:

• Grey: 18 times
• White: 13 times
• Black: 9 times

To find the experimental probability of landing on black or white:

1. Number of black and white spins: 9 (black) + 13 (white) = 22
2. Total spins: 40

The experimental probability $P(\text{Black or White})$ is: $P(\text{Black or White}) = \frac{22}{40} = 0.55$

(c) True Statement

Given a large number of spins, the law of large numbers states that the experimental probability will approach the theoretical probability. However, there can still be small differences due to random variation.

So, the correct statement is:

• "With a large number of spins, there might be a difference between the experimental and theoretical probabilities, but the difference should be small."

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

Here are some related questions you might find interesting:

1. How do you calculate the theoretical probability of an event?
2. What factors can cause a difference between theoretical and experimental probabilities?
3. How does increasing the number of trials affect the experimental probability?
4. Can a spinner be considered fair if the experimental probabilities differ significantly from the theoretical probabilities?
5. What is the law of large numbers in probability theory?
6. How would the probabilities change if the spinner had more slices of one color?
7. What other factors can influence the outcomes in experiments involving randomness?
8. How can you use probability to predict outcomes in real-world scenarios?

Tip: In probability, always verify if events are equally likely when calculating theoretical probabilities.