There are seven white and one brown eggs in an egg box. Ruchira decides to make a two-egg omeltte. She takes out each egg from the box without looking at its colour. What is the probability that Ruchira gets an omellete made from
two white eggs

Answer

To solve the problem of finding the probability that Ruchira gets an omelette made from two white eggs, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Number of Eggs:**
- There are 7 white eggs and 1 brown egg in the box.
- Total number of eggs = 7 (white) + 1 (brown) = 8 eggs.

2. **Determine the Total Ways to Choose 2 Eggs:**
- The total number of ways to choose 2 eggs from 8 eggs can be calculated using the combination formula:
\[ \text{Total ways to choose 2 eggs} = \binom{8}{2} = \frac{8 \times 7}{2 \times 1} = 28 \]

3. **Determine the Number of Favorable Outcomes (Choosing 2 White Eggs):**
- The number of ways to choose 2 white eggs from 7 white eggs:
\[ \text{Ways to choose 2 white eggs} = \binom{7}{2} = \frac{7 \times 6}{2 \times 1} = 21 \]

4. **Calculate the Probability:**
- The probability of choosing 2 white eggs can be calculated by dividing the number of favorable outcomes by the total outcomes:
\[ \text{Probability of 2 white eggs} = \frac{\text{Ways to choose 2 white eggs}}{\text{Total ways to choose 2 eggs}} = \frac{21}{28} \]
- Simplifying the fraction:
\[ \frac{21}{28} = \frac{3}{4} \]

### Final Answer:
The probability that Ruchira gets an omelette made from two white eggs is \(\frac{3}{4}\).

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