If seven slips of paper are labelled as 1, 2, 3, 4, 6, 7, 8 and one slip is drawn out of it, then what is the probability that it is
(i) a 7 ?
(ii) greater than 4?
(iii) an odd number?

Options

A. `{:(i,ii,iii,),(1//7,3//7,4//7,):}`
B. `{:(i,ii,iii,),(1//7,3//7,3//7,):}`
C. `{:(i,ii,iii,),(1//7,2//7,5//7,):}`
D. `{:(i,ii,iii,),(1//7,5//7,2//7,):}`

Answer

To solve the problem, we need to determine the probability for three different scenarios based on the slips of paper labeled 1, 2, 3, 4, 6, 7, and 8.

### Total Outcomes:
The total number of slips is 7, which are labeled as follows:
1, 2, 3, 4, 6, 7, 8

### (i) Probability of drawing a 7:
1. **Identify the favorable outcome**: The only favorable outcome for this event is the slip labeled '7'.
2. **Count the favorable outcomes**: There is 1 favorable outcome (the slip labeled '7').
3. **Calculate the probability**:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{1}{7} \]

### (ii) Probability of drawing a number greater than 4:
1. **Identify the favorable outcomes**: The numbers greater than 4 from the slips are 6, 7, and 8.
2. **Count the favorable outcomes**: There are 3 favorable outcomes (6, 7, 8).
3. **Calculate the probability**:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{7} \]

### (iii) Probability of drawing an odd number:
1. **Identify the favorable outcomes**: The odd numbers from the slips are 1, 3, and 7.
2. **Count the favorable outcomes**: There are 3 favorable outcomes (1, 3, 7).
3. **Calculate the probability**:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{7} \]

### Summary of Probabilities:
- (i) Probability of drawing a 7: \(\frac{1}{7}\)
- (ii) Probability of drawing a number greater than 4: \(\frac{3}{7}\)
- (iii) Probability of drawing an odd number: \(\frac{3}{7}\)