Cards numbered 7 to 40 were put in a box . Poonam selects a card at random .What is the probability that Poonam selects a card which is a multiple of 7 ?

Answer

To solve the problem of finding the probability that Poonam selects a card which is a multiple of 7 from cards numbered 7 to 40, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Range of Cards**:
The cards are numbered from 7 to 40.

2. **Count the Total Number of Cards**:
The total number of cards can be calculated as follows:
\[ \text{Total Cards} = 40 - 7 + 1 = 34 \]

3. **List the Multiples of 7 within the Range**:
We need to find the multiples of 7 between 7 and 40. The multiples of 7 in this range are:
- 7 (7 × 1)
- 14 (7 × 2)
- 21 (7 × 3)
- 28 (7 × 4)
- 35 (7 × 5)

The next multiple, 42 (7 × 6), is not included since it exceeds 40.

4. **Count the Favorable Outcomes**:
From the list above, we have the following multiples of 7:
- 7, 14, 21, 28, 35

Thus, the number of favorable outcomes (multiples of 7) is 5.

5. **Calculate the Probability**:
The probability \( P \) of selecting a card that is a multiple of 7 is given by the formula:
\[ P(\text{multiple of 7}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}} = \frac{5}{34} \]

### Final Answer:
The probability that Poonam selects a card which is a multiple of 7 is \( \frac{5}{34} \).

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