Final answer:
It is very likely to obtain identical restriction fragments using the restriction enzyme EcoRI due to its high specificity for the palindromic sequence 5' GAATTC 3', creating predictable sticky ends useful in molecular cloning and recombinant DNA technology.
Step-by-step explanation:
The likelihood of obtaining identical restriction fragments using the restriction enzyme EcoRI is very likely because EcoRI has high specificity for its recognition sequence. EcoRI recognizes and cuts DNA at the specific palindromic sequence 5' GAATTC 3'. As such, every time this specific sequence appears in the DNA, EcoRI will cleave it, creating predictable sticky ends. These ends are 'sticky' because they can base pair with complementary sequences of DNA fragments also cut by EcoRI, which is particularly useful in the processes of molecular cloning and recombinant DNA technology. Therefore, the correct answer to the question about the likelihood that identical restriction fragments would be obtained is (c) Very likely, as EcoRI has high specificity.