To find the probability that the product of two randomly chosen whole numbers is divisible by 5, we can follow these steps:
### Step 1: Identify the whole numbers
The whole numbers we are considering are from 0 to 9, which gives us a total of 10 whole numbers: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.
### Step 2: Determine when the product is divisible by 5
A product of two numbers is divisible by 5 if at least one of the numbers is divisible by 5. The numbers from our set that are divisible by 5 are 0 and 5.
### Step 3: Calculate the total number of outcomes
Since we are choosing two numbers, the total number of outcomes when selecting two numbers from the set is:
\[
10 \times 10 = 100
\]
This is because there are 10 choices for the first number and 10 choices for the second number.
### Step 4: Calculate the favorable outcomes
Now, we need to calculate the number of favorable outcomes where the product is divisible by 5.
1. **Case 1**: If the first number is **0**:
- The second number can be any of the 10 numbers (0 through 9).
- Favorable outcomes = 10.
2. **Case 2**: If the first number is **5**:
- The second number can also be any of the 10 numbers (0 through 9).
- Favorable outcomes = 10.
3. **Case 3**: If the first number is **1, 2, 3, 4, 6, 7, 8, or 9** (8 cases):
- In each of these cases, the second number must be either **0** or **5** to ensure the product is divisible by 5.
- For each of these 8 numbers, there are 2 favorable outcomes (0 or 5).
- Total favorable outcomes from these cases = \(8 \times 2 = 16\).
### Step 5: Sum the favorable outcomes
Now, we can sum the favorable outcomes from all cases:
\[
\text{Total favorable outcomes} = 10 \text{ (from case 1)} + 10 \text{ (from case 2)} + 16 \text{ (from case 3)} = 36.
\]
### Step 6: Calculate the probability
The probability that the product of the two chosen numbers is divisible by 5 is given by the formula:
\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{36}{100} = \frac{9}{25}.
\]
### Final Answer
The probability that the product of two randomly chosen whole numbers is divisible by 5 is:
\[
\frac{9}{25}.
\]
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