A box contains cards numbered from 11 to 123. A card is drawn at random from the box. Find the probability that the number on the drawn card is:
a multiple of 7.

Answer

To find the probability that the number on the drawn card is a multiple of 7, we will follow these steps:

### Step 1: Determine the total number of cards
The cards are numbered from 11 to 123. To find the total number of cards, we can use the formula:

\[ \text{Total Cards} = \text{Last Number} - \text{First Number} + 1 \]

Substituting the values:

\[ \text{Total Cards} = 123 - 11 + 1 = 113 \]

### Step 2: Identify the multiples of 7 between 11 and 123
Next, we will find the multiples of 7 that fall within the range of 11 to 123. The multiples of 7 can be calculated as follows:

- The smallest multiple of 7 greater than or equal to 11 is 14 (7 x 2).
- The largest multiple of 7 less than or equal to 123 is 119 (7 x 17).

Now we can list the multiples of 7 between 14 and 119:

- 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119

### Step 3: Count the favorable outcomes
Now we count the multiples of 7 that we have listed:

- The multiples of 7 between 11 and 123 are: 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119.

This gives us a total of 16 favorable outcomes.

### Step 4: Calculate the probability
The probability \( P \) of drawing a card that is a multiple of 7 can be calculated using the formula:

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

Substituting the values we found:

\[ P(\text{multiple of 7}) = \frac{16}{113} \]

### Final Answer
Thus, the probability that the number on the drawn card is a multiple of 7 is:

\[ \frac{16}{113} \]

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