Let's break down and solve the two parts of this problem.

Part (a): Probability of Winning a Prize

The prize wheel is divided into 20 equal sections, and only one section will result in a win. Since the wheel is fair, each section has an equal probability of being landed on.

The probability $P$ of winning a prize is given by:

$P = \frac{\text{Number of winning sections}}{\text{Total number of sections}} = \frac{1}{20}$

Thus, the probability of winning a prize in one spin is $\frac{1}{20}$.

Part (b): Expected Number of People Winning a Prize

If 360 people each spin the wheel once, the expected number of people who will win a prize is found by multiplying the total number of people by the probability of winning.

$\text{Expected number of winners} = 360 \times \frac{1}{20} = 18$

So, we expect 18 people to win a prize if 360 people spin the wheel once.

Would you like more details or have any questions?

Here are 5 related questions you can explore:

1. What is the probability of not winning a prize in a single spin?
2. If 500 people spin the wheel, what is the expected number of winners?
3. How does the expected number of winners change if the probability of winning is increased to $\frac{2}{20}$?
4. What is the probability that exactly 2 people win in 10 spins of the wheel?
5. How does the expected number of winners change if the number of sections is increased to 25?

Tip: In probability, the expected value gives a prediction of the average outcome over many trials or repetitions.