The examinee could guess . . . . . . . . the answer correctly.

The other options are incorrect because they do not accurately reflect the meaning of the sentence.

• The word “with” is used to indicate that something is done with the help of something else. In this case, the examinee did not need help to guess the answer.
• The word “of” is used to indicate that something is a part of something else. In this case, the answer was not a part of the question.
• The word “at” is used to indicate a location or position. In this case, the answer was not a location or position.