A two digits number is chosen at random. Find the probability that it is a multiple of 7.

Options

A. `(11)/(90)`
B. `(13)/(90)`
C. `(7)/(45)`
D. `(8)/(45)`

Explanation

To solve the problem of finding the probability that a randomly chosen two-digit number is a multiple of 7, we will follow these steps:

### Step 1: Identify the range of two-digit numbers
The two-digit numbers range from 10 to 99.

### Step 2: Count the total number of two-digit numbers
To find the total number of two-digit numbers, we calculate:
- The smallest two-digit number is 10.
- The largest two-digit number is 99.

Total two-digit numbers = 99 - 10 + 1 = 90.

### Step 3: Identify the multiples of 7 within the two-digit range
We need to find the multiples of 7 that fall between 10 and 99.

- The smallest two-digit multiple of 7 is 14 (7 × 2).
- The largest two-digit multiple of 7 is 98 (7 × 14).

### Step 4: List the multiples of 7 from 14 to 98
The multiples of 7 between 14 and 98 are:
- 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98.

### Step 5: Count the number of multiples of 7
Counting the numbers listed above, we find there are 13 multiples of 7.

### Step 6: Calculate the probability
The probability \( P \) that a randomly chosen two-digit number is a multiple of 7 is given by the formula:

\[ P(\text{multiple of 7}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{13}{90} \]

### Final Answer
Thus, the probability that a randomly chosen two-digit number is a multiple of 7 is \( \frac{13}{90} \).

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