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.