To solve the problem step by step, we will calculate the probabilities for each of the four parts of the question regarding the cards numbered from 11 to 60.
### Total Number of Cards
First, we need to determine the total number of cards in the box. The cards are numbered from 11 to 60.
1. **Total Cards Calculation**:
\[
\text{Total Cards} = 60 - 11 + 1 = 50
\]
### (i) Probability of Drawing an Odd Number
Next, we will find the probability of drawing an odd number.
2. **List of Odd Numbers**:
The odd numbers between 11 and 60 are:
11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59.
**Count of Odd Numbers**:
There are 25 odd numbers.
3. **Probability Calculation**:
\[
P(\text{Odd Number}) = \frac{\text{Number of Odd Numbers}}{\text{Total Cards}} = \frac{25}{50} = \frac{1}{2}
\]
### (ii) Probability of Drawing a Perfect Square Number
Now, we will find the probability of drawing a perfect square number.
4. **List of Perfect Squares**:
The perfect squares between 11 and 60 are:
16 (4²), 25 (5²), 36 (6²), 49 (7²).
**Count of Perfect Squares**:
There are 4 perfect square numbers.
5. **Probability Calculation**:
\[
P(\text{Perfect Square}) = \frac{\text{Number of Perfect Squares}}{\text{Total Cards}} = \frac{4}{50} = \frac{2}{25}
\]
### (iii) Probability of Drawing a Number Divisible by 5
Next, we will find the probability of drawing a number that is divisible by 5.
6. **List of Numbers Divisible by 5**:
The numbers divisible by 5 between 11 and 60 are:
15, 20, 25, 30, 35, 40, 45, 50, 55.
**Count of Numbers Divisible by 5**:
There are 9 numbers.
7. **Probability Calculation**:
\[
P(\text{Divisible by 5}) = \frac{\text{Number of Divisible by 5}}{\text{Total Cards}} = \frac{9}{50} = \frac{9}{50}
\]
### (iv) Probability of Drawing a Prime Number Less than 20
Finally, we will find the probability of drawing a prime number less than 20.
8. **List of Prime Numbers Less than 20**:
The prime numbers less than 20 are:
11, 13, 17, 19.
**Count of Prime Numbers**:
There are 4 prime numbers.
9. **Probability Calculation**:
\[
P(\text{Prime Number < 20}) = \frac{\text{Number of Prime Numbers}}{\text{Total Cards}} = \frac{4}{50} = \frac{2}{25}
\]
### Summary of Probabilities
- (i) Probability of an odd number: \( \frac{1}{2} \)
- (ii) Probability of a perfect square: \( \frac{2}{25} \)
- (iii) Probability of a number divisible by 5: \( \frac{9}{50} \)
- (iv) Probability of a prime number less than 20: \( \frac{2}{25} \)
