What is the probability of selecting two fresh eggs simultaneously from Tray A, given there are only two trays: Tray A and Tray B?

Consider the following statements:

**Statement I:** Tray B contains 30 eggs with fresh and rotten eggs in the ratio 7 : 3. The ratio of fresh eggs in Tray A to Tray B is 2 : 3.

**Statement II:** Tray A contains 20 eggs in total, out of which 14 are fresh and the rest are rotten.

**Statement III:** Tray B contains 30 eggs and Tray A contains 20 eggs. The ratio of rotten eggs to fresh eggs in Tray A is 3 : 7.

Which of the above statements is/are sufficient to answer the question?

Question

What is the probability of selecting two fresh eggs simultaneously from Tray A, given there are only two trays: Tray A and Tray B?

Consider the following statements:

**Statement I:** Tray B contains 30 eggs with fresh and rotten eggs in the ratio 7 : 3. The ratio of fresh eggs in Tray A to Tray B is 2 : 3.

**Statement II:** Tray A contains 20 eggs in total, out of which 14 are fresh and the rest are rotten.

**Statement III:** Tray B contains 30 eggs and Tray A contains 20 eggs. The ratio of rotten eggs to fresh eggs in Tray A is 3 : 7.

Which of the above statements is/are sufficient to answer the question?

Accepted Answer

**Solution:**

1. The question asks for the probability of selecting two fresh eggs simultaneously from Tray A.

2. To find this probability, we need to know the total number of eggs in Tray A and how many of them are fresh.

3. **Analyzing Statement I:**
   - Tray B has 30 eggs with fresh:rotten = 7:3.
   - Ratio of fresh eggs in Tray A to Tray B is 2:3.
   - However, the total number of eggs in Tray A is unknown, so we cannot determine the exact number of fresh eggs in Tray A.
   - Hence, Statement I alone is insufficient.

4. **Analyzing Statement II:**
   - Tray A has 20 eggs in total, with 14 fresh eggs.
   - This directly gives us the number of fresh eggs and total eggs in Tray A.
   - Using this, probability of choosing two fresh eggs from Tray A can be calculated.
   - Therefore, Statement II alone is sufficient.

5. **Analyzing Statement III:**
   - Tray B has 30 eggs, Tray A has 20 eggs.
   - Ratio of rotten to fresh eggs in Tray A is 3:7.
   - Total parts = 3 + 7 = 10 parts.
   - Fresh eggs in Tray A = (7/10) × 20 = 14.
   - Total eggs in Tray A = 20.
   - This also provides the exact number of fresh eggs in Tray A.
   - Hence, Statement III alone is sufficient.

6. Since either Statement II or Statement III alone is sufficient to answer the question, the correct choice is "Either II or III".

**Answer:** Either II or III

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