Introduction:
In DNA replication, both strands of the DNA molecule are labeled with radioactive thymidine. When these labeled strands are allowed to duplicate in an environment containing non-radioactive thymidine, the number of DNA molecules that will contain radioactive thymidine after three duplications can be determined.

Explanation:
To understand the number of DNA molecules with radioactive thymidine after three duplications, let's break down the process into three stages:

Stage 1: Initial DNA Molecule:
At the start, we have a single DNA molecule with both strands labeled with radioactive thymidine.

Stage 2: First Duplication:
During the first duplication, the DNA molecule unwinds and each strand serves as a template for the synthesis of a new complementary strand. Since the environment contains non-radioactive thymidine, the newly synthesized strands will not be labeled with radioactivity. Thus, after the first duplication, we have:

- Two DNA molecules, each consisting of one original radioactive strand and one newly synthesized non-radioactive strand.

Stage 3: Second Duplication:
During the second duplication, the two DNA molecules from the first duplication serve as templates for the synthesis of new complementary strands. The radioactive thymidine in the original strands of both DNA molecules will be replicated, resulting in:

- Two DNA molecules, each containing one original radioactive strand and one newly synthesized radioactive strand.
- Two DNA molecules, each containing one original non-radioactive strand and one newly synthesized non-radioactive strand.

Stage 4: Third Duplication:
During the third duplication, the four DNA molecules from the second duplication serve as templates for the synthesis of new complementary strands. The radioactive thymidine in the original strands of two DNA molecules will be replicated, resulting in:

- Four DNA molecules, each containing one original radioactive strand and two newly synthesized radioactive strands.
- Two DNA molecules, each containing one original non-radioactive strand and two newly synthesized non-radioactive strands.

Final Result:
After three duplications, we have a total of 6 DNA molecules. Out of these 6 DNA molecules, only 2 contain radioactive thymidine. Therefore, the correct answer is between 2.0 and 2.0, indicating that exactly 2 DNA molecules will contain radioactive thymidine after three duplications.

Conclusion:
When both strands of a DNA molecule labeled with radioactive thymidine are allowed to duplicate in an environment containing non-radioactive thymidine, after three duplications, the number of DNA molecules containing radioactive thymidine is 2.