Answer:
The chance of each nucleotide base (A, T, C, or G) occurring in a random sequence is 1/4. Since there are six nucleotide pairs in the restriction site, the probability of each pair matching is (1/4)2 = 1/16. Therefore, the probability of all six adjacent nucleotide pairs matching the restriction site is (1/16)6 = 1/16777216, which is approximately 1 in 16 million.
However, none of the given answer options is correct. The closest answer is d) (1/4)6 = 1/4096, which is the probability of a randomly selected sequence of six nucleotide pairs matching a specific sequence of six pairs. But the restriction site can match in any order, so we need to consider all the possible combinations of six adjacent pairs in the DNA sequence.
There are (2n-6+1) possible locations for a six-nucleotide pair sequence in a double-stranded DNA molecule of length n. For n = 6, there is only one possible location, but for larger values of n, there are more possibilities. For example, in a molecule of length 10, there are five possible locations:
ATGCAGTACC
TGCAGTA
CAGTAC
GTACC
TACCA
So the probability of at least one of these locations matching the restriction site is 1 - (1 - 1/4096)5 = 0.00122, which is approximately 1 in 820.
Therefore, the correct answer is not listed among the given options.