Question

I mistook that woman _ a maid

Answer 1

I mistook that woman as a maid....

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Answer 2

Here, in this question, it wants us to put in the necessary as well as the suitable preposition in order to place a connection between the first part and the second. Moreover, preposition helps in indicating some relationship between a noun or pronoun and some other word within the same sentence.

I mistook that woman for a maid.

For is utilized here in order to represent the relationship between the common noun woman and maid.