What Percentage of Random DNA Sequences Does BamH1 Recognize?

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The discussion centers on calculating the percentage of random 6 bp DNA sequences that the restriction enzyme BamH1 recognizes, specifically the sequence GGATCC. The proposed answer is 0.02%, derived from the probability of randomly synthesizing that exact sequence, calculated as (1/4)^6. This reasoning is based on the four possible nucleotides (A, T, C, G) for each position in the sequence. The participant seeks confirmation of this calculation. The conclusion is that the probability of encountering the BamH1 recognition site in random DNA sequences is indeed very low.
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Homework Statement



A library of randomly synthesized duplex DNA strands (length = 6 bp) is generated.
What percentage of these sequences would you expect that the restriction enzyme BamH1 (restriction site = GGATCC) would recognize?
a. 0%
b. 0.02%
c. 0.48%
d. 0.07%


Homework Equations


N/A


The Attempt at a Solution


I think that the answer is b, but I'm just looking for confirmation. My reasoning is that there are 4 possible codons, A,T,C,G and so the chance that a randomly synthesized DNA strand of exactly GGATCC would simply be (1/4)^6 or 0.02%
 
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Seems fine to me.
 
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