The correct answer is: D. may have been
The sentence “We might have been visited the sick man if we knew that he was in the hospital” is in the past modal perfect. This tense is used to talk about something that was possible or likely to happen in the past but did not happen. The modal verb “might” expresses possibility or likelihood, and the past perfect “had been” indicates that the action of visiting the sick man was not completed.
The other options are incorrect because they do not express possibility or likelihood. Option A, “would have been”, is in the past perfect conditional. This tense is used to talk about something that was possible or likely to happen in the past but did not happen, and the consequence of that action not happening. Option B, “will have”, is in the future perfect. This tense is used to talk about something that will be completed by a certain time in the future. Option C, “would have”, is in the past simple conditional. This tense is used to talk about something that was possible or likely to happen in the past but did not happen. Option E, “No correction required”, is incorrect because the sentence does need to be corrected.