[trowftd]

Aren't you miscounting though? 111 contains the 11 sequence twice.

[azernik]

Which is probably the key intuition here - the expected number of matches is exactly the same, but because you can have more matches for the purely-repeated sequence in the same string the total number of strings containing those matches is smaller.

[panic]

Sure, but the question is "how likely" not "how many times". Counting the expected number of times is a much easier problem because you can use the linearity of expectation.

[jstanley]

But you're trying to find a bit-substring of length 2 that is least likely to have been transmitted.

If the bit strings of length 3 are chosen uniformly, 11 is less likely to appear than 10.

[bhouston]

You are totally right. He is incorrect.