Select the option that best replaces the phrase in quotes. 

Many people mistake familiarity for a vulgar style, and suppose that to write without affectation 'is to write at random speed'.

Option C and Option D are incorrect as the author talks about writing without affectation i.e. writing without any pretension. Hence, it can be mistaken for writing without consideration or care and not writing fast. 

Between options A and B, A contains the correct phrase 'at random'. The phrase means without a care and in a disorderly manner. "Writing  randomly" does not carry the same implication. Also, here the modifier 'random' is a misplaced modifier. It is modifying the way of writing instead of modifying what is written.