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# How many times will EcoR1 cut a random 10kb DNA fragment? How does this change for linear or circular DNA?

Here's my initial answer. Requires refining from someone who understands probability better.

Each base can be ATCG. (4 possibilities)

EcoR1 recognizes a 6bp sequence, which is one out of 4^6 possibilities.

So for a 10kb linear fragment, there are (10k-5) such possibilities.

So number of cuts is 9995/(4^6)?

Or is there a better way to answer this?