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Let's analyze the problem.

### Problem Summary:
You have a probability distribution table for the random variable \( Y \), representing the number of major hurricanes (Category 3 or higher) striking a region per year. The table provides the probability \( P(Y = y) \) for different values of \( y \), which corresponds to the number of hurricanes.

### Part (a) - Task:
You are asked to use random-variable notation to represent the event where the year had at least one major hurricane.

#### Solution:
1. To represent the event that "the year had at least one major hurricane," we use the random variable \( Y \).
2. The condition "at least one major hurricane" implies that \( Y \geq 1 \).
3. The notation for this event can be written as \( P(Y \geq 1) \).

Now, looking at the answer choices:
- **Option A**: Likely suggests filling in a general event notation, such as \( Y \geq 1 \).
- **Option B**: Suggests filling in the probability notation, such as \( P(Y \geq 1) \).

Since the question specifically asks for "random-variable notation," **Option B** is correct with \( P(Y \geq 1) \).

Therefore, you should select **Option B** and fill in \( P(Y \geq 1) \).

Would you like further details on this solution, or have any other questions? 

Here are five additional related questions for practice:
1. How would you calculate \( P(Y \geq 1) \) using the provided probability distribution?
2. What is the probability that no hurricanes (Category 3 or higher) will strike in a given year?
3. How would you represent the event that exactly two hurricanes will occur in a given year?
4. How do you interpret a cumulative probability distribution in this context?
5. How would you calculate the expected number of hurricanes per year using this distribution?

**Tip:** For events defined by inequalities, always check the problem context to see if cumulative probabilities or simple probabilities are needed.

Use random-variable notation to represent the event that the year had at least one major hurricane. Select the correct choice below and fill in the answer box within your choice.

Learn how to represent the probability of at least one major hurricane using random-variable notation. This problem covers probability distribution for a discrete random variable and is ideal for college students studying introductory statistics.

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