What is the probability that a randomly selected factor for a positive factors of 72 is less than 11?

Options

A. `(5)/(12)`
B. `(7)/(11)`
C. `(7)/(12)`
D. `(7)/(10)`

Answer

To find the probability that a randomly selected factor of 72 is less than 11, we can follow these steps:

### Step 1: Find the factors of 72
First, we need to determine all the positive factors of the number 72. The factors of 72 are:
- 1
- 2
- 3
- 4
- 6
- 8
- 9
- 12
- 18
- 24
- 36
- 72

### Step 2: Count the total number of factors
Now, we count the total number of factors we found:
- Total number of factors = 12

### Step 3: Identify the factors less than 11
Next, we need to find which of these factors are less than 11. The factors of 72 that are less than 11 are:
- 1
- 2
- 3
- 4
- 6
- 8
- 9

### Step 4: Count the number of favorable outcomes
Now, we count how many factors are less than 11:
- Number of favorable outcomes = 7

### Step 5: Calculate the probability
Finally, we can calculate the probability using the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Substituting the values we found:
\[ \text{Probability} = \frac{7}{12} \]

### Final Answer
The probability that a randomly selected factor of 72 is less than 11 is \( \frac{7}{12} \).

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