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
one white and one brown egg

Answer

To find the probability that Ruchira gets an omelette made from one white egg and one brown egg, we can follow these steps:

### Step 1: Identify the total number of eggs
There are 7 white eggs and 1 brown egg in the egg box. Therefore, the total number of eggs is:
\[ \text{Total eggs} = 7 \text{ (white)} + 1 \text{ (brown)} = 8 \text{ eggs} \]

**Hint:** Count the total number of items in the set to understand the sample space.

### Step 2: Determine the favorable outcomes
We need to consider the two scenarios in which Ruchira can pick one white egg and one brown egg:
1. She picks a white egg first and then a brown egg.
2. She picks a brown egg first and then a white egg.

### Step 3: Calculate the probability for each scenario
**Scenario 1:** Picking a white egg first and then a brown egg.
- The probability of picking a white egg first:
\[ P(\text{White first}) = \frac{7}{8} \]
- After picking a white egg, there are now 7 eggs left (6 white and 1 brown). The probability of then picking a brown egg:
\[ P(\text{Brown second | White first}) = \frac{1}{7} \]
- Therefore, the probability for this scenario is:
\[ P(\text{White first and Brown second}) = P(\text{White first}) \times P(\text{Brown second | White first}) = \frac{7}{8} \times \frac{1}{7} = \frac{1}{8} \]

**Scenario 2:** Picking a brown egg first and then a white egg.
- The probability of picking a brown egg first:
\[ P(\text{Brown first}) = \frac{1}{8} \]
- After picking a brown egg, there are now 7 eggs left (7 white). The probability of then picking a white egg:
\[ P(\text{White second | Brown first}) = \frac{7}{7} = 1 \]
- Therefore, the probability for this scenario is:
\[ P(\text{Brown first and White second}) = P(\text{Brown first}) \times P(\text{White second | Brown first}) = \frac{1}{8} \times 1 = \frac{1}{8} \]

### Step 4: Add the probabilities of both scenarios
Now we can find the total probability of getting one white egg and one brown egg by adding the probabilities of both scenarios:
\[ P(\text{One white and one brown}) = P(\text{White first and Brown second}) + P(\text{Brown first and White second}) \]
\[ P(\text{One white and one brown}) = \frac{1}{8} + \frac{1}{8} = \frac{2}{8} = \frac{1}{4} \]

### Final Answer
The probability that Ruchira gets an omelette made from one white egg and one brown egg is:
\[ \frac{1}{4} \]

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