Ten cards are numbered as 1,2,3,4,5………….10 respectively. They are kept in a box and mixed throughly. One card is chosen at random from the box. What is the probability of (i) getting the number 8? (ii) getting a number less than 5? (iii) getting a number greater than 4? (iv) getting a 1-digit number?

Answer

To solve the problem step by step, we will calculate the probability for each part of the question.

### Given:
- Total cards = 10 (numbered 1 to 10)
- Sample space (S) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

### Probability Formula:
The probability (P) of an event is given by the formula:
\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

### Part (i): Probability of getting the number 8
1. **Identify the favorable outcome**: The only favorable outcome for this event is the card numbered 8. So, the number of favorable outcomes = 1.
2. **Total outcomes**: There are 10 cards in total.
3. **Calculate the probability**:
\[ P(\text{getting 8}) = \frac{1}{10} \]

### Part (ii): Probability of getting a number less than 5
1. **Identify the favorable outcomes**: The numbers less than 5 are {1, 2, 3, 4}. So, the number of favorable outcomes = 4.
2. **Total outcomes**: There are still 10 cards in total.
3. **Calculate the probability**:
\[ P(\text{getting a number less than 5}) = \frac{4}{10} = \frac{2}{5} \]

### Part (iii): Probability of getting a number greater than 4
1. **Identify the favorable outcomes**: The numbers greater than 4 are {5, 6, 7, 8, 9, 10}. So, the number of favorable outcomes = 6.
2. **Total outcomes**: There are still 10 cards in total.
3. **Calculate the probability**:
\[ P(\text{getting a number greater than 4}) = \frac{6}{10} = \frac{3}{5} \]

### Part (iv): Probability of getting a 1-digit number
1. **Identify the favorable outcomes**: All the cards numbered from 1 to 9 are 1-digit numbers. So, the favorable outcomes are {1, 2, 3, 4, 5, 6, 7, 8, 9}. Thus, the number of favorable outcomes = 9.
2. **Total outcomes**: There are still 10 cards in total.
3. **Calculate the probability**:
\[ P(\text{getting a 1-digit number}) = \frac{9}{10} \]

### Summary of Answers:
- (i) Probability of getting the number 8: \( \frac{1}{10} \)
- (ii) Probability of getting a number less than 5: \( \frac{2}{5} \)
- (iii) Probability of getting a number greater than 4: \( \frac{3}{5} \)
- (iv) Probability of getting a 1-digit number: \( \frac{9}{10} \)