Two whole numbers are randomly chosen and multiplied, then the chance that their product is divisible by 5 is

Options

A. `(4)/(25)`
B. `(9)/(25)`
C. `(16)/(25)`
D. `(1)/(25)`

Answer

To find the probability that the product of two randomly chosen whole numbers is divisible by 5, we can follow these steps:

### Step 1: Understanding the Problem
We need to determine the conditions under which the product of two whole numbers is divisible by 5. A product is divisible by 5 if at least one of the numbers is divisible by 5.

### Step 2: Identifying Whole Numbers
Whole numbers include 0, 1, 2, 3, ..., 9 (for simplicity, we will consider numbers from 0 to 9). This gives us a total of 10 whole numbers.

### Step 3: Counting Favorable Outcomes
To find the probability, we need to count how many combinations of two numbers yield a product divisible by 5.

1. **When one of the numbers is 0**: The product will be 0, which is divisible by 5. If the first number is 0, the second number can be any of the 10 numbers (0 to 9). This gives us 10 combinations.

2. **When one of the numbers is 5**: If the first number is 5, the second number can again be any of the 10 numbers (0 to 9). This gives us another 10 combinations.

3. **When one of the numbers is 10 or more**: Since we are only considering numbers from 0 to 9, we do not have any numbers greater than 9.

### Step 4: Counting Non-Divisible Outcomes
Next, we need to count how many combinations do not yield a product divisible by 5. This occurs when neither number is 0 or 5.

- The numbers that are not divisible by 5 from 0 to 9 are: 1, 2, 3, 4, 6, 7, 8, 9 (total 8 numbers).
- The combinations of these numbers (not including 0 or 5) can be calculated as follows:
- Total combinations of two numbers from these 8 numbers = 8 * 8 = 64.

### Step 5: Total Outcomes
The total number of outcomes when choosing two numbers from 0 to 9 is:
- Total outcomes = 10 * 10 = 100.

### Step 6: Calculating Favorable Outcomes
Now, we can calculate the total favorable outcomes:
- Total favorable outcomes = Total outcomes - Non-divisible outcomes
- Total favorable outcomes = 100 - 64 = 36.

### Step 7: Calculating Probability
Now we can calculate the probability that the product is divisible by 5:
- Probability = (Number of favorable outcomes) / (Total outcomes)
- Probability = 36 / 100 = 9 / 25.

### Final Answer
The probability that the product of two randomly chosen whole numbers is divisible by 5 is **9/25**.

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