A game of numbers has cards marked with 11, 12, 13, ……, 40. A card is drawn at random. Find the probability that the number on the card drawn is :
(ii) Divisible by 7

Answer

To solve the problem, we need to find the probability that a card drawn at random from a set of cards numbered 11 to 40 has a number that is divisible by 7.

### Step-by-Step Solution:

1. **Identify the Range of Numbers:**
The cards are marked with numbers from 11 to 40.
- The total numbers in this range can be calculated as:
\[ \text{Total numbers} = 40 - 11 + 1 = 30 \]

**Hint:** Count the total numbers by subtracting the smallest number from the largest and adding one.

2. **List the Numbers Divisible by 7:**
We need to find the numbers in the range from 11 to 40 that are divisible by 7.
- The multiples of 7 are: 7, 14, 21, 28, 35, 42, etc.
- From this list, the numbers that fall within our range (11 to 40) are:
- 14 (7 × 2)
- 21 (7 × 3)
- 28 (7 × 4)
- 35 (7 × 5)

**Hint:** To find multiples of 7, multiply 7 by integers starting from 2 until you exceed 40.

3. **Count the Favorable Outcomes:**
From the list above, the favorable outcomes (numbers divisible by 7) are 14, 21, 28, and 35.
- Therefore, the number of favorable outcomes is 4.

**Hint:** Count how many numbers you found that meet the criteria.

4. **Calculate the Probability:**
The probability \( P \) of drawing a card with a number that is divisible by 7 can be calculated using the formula:
\[ P(\text{Divisible by 7}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{4}{30} \]
- Simplifying this fraction:
\[ P(\text{Divisible by 7}) = \frac{2}{15} \]

**Hint:** Remember that probability is a ratio of favorable outcomes to total outcomes, and simplify the fraction if possible.

### Final Answer:
The probability that the number on the card drawn is divisible by 7 is \( \frac{2}{15} \).