I think you need some other stuff in there to have a clear sentence, say: I think at least one of the reason s that Mike gave for being late was credible. I think one of the reason s that Mike gave for being late was credible. I think only a reason that Mike gave for being late was credible.
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Here, I think you can make it 'a reason' if the writer is thinking or coming from the "multiple reasons" point of view