The weather report for today states that there is a `40%` chance of sun, a `25%` chance of rain, and a `35%` chance of hail. Assuming only one of the three out - comes can happen, what is the probability that it rains or hails today?

Options

A. 35%
B. 25%
C. 40%
D. 60%

Answer

To find the probability that it rains or hails today, we can follow these steps:

### Step 1: Identify the probabilities given in the problem.
- Probability of sun (P(Sun)) = 40% = 0.40
- Probability of rain (P(Rain)) = 25% = 0.25
- Probability of hail (P(Hail)) = 35% = 0.35

### Step 2: Understand the requirement of the problem.
We need to find the probability that it rains or hails today. This can be expressed mathematically as:
\[ P(Rain \cup Hail) = P(Rain) + P(Hail) \]

### Step 3: Substitute the values into the equation.
We know:
- \( P(Rain) = 0.25 \)
- \( P(Hail) = 0.35 \)

Now, substituting these values:
\[ P(Rain \cup Hail) = P(Rain) + P(Hail) \]
\[ P(Rain \cup Hail) = 0.25 + 0.35 \]

### Step 4: Perform the addition.
Now, we add the probabilities:
\[ P(Rain \cup Hail) = 0.25 + 0.35 = 0.60 \]

### Step 5: Convert the probability back to percentage.
To express the probability as a percentage, we multiply by 100:
\[ P(Rain \cup Hail) = 0.60 \times 100 = 60\% \]

### Final Answer:
The probability that it rains or hails today is **60%**.

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