If the labels are guaranteed to be wrong, then you simply pluck a ball from the bin labeled "mixed". You know it's not mixed, since the label is wrong. Say you

If the labels are guaranteed to be wrong, then you simply pluck a ball from the bin labeled "mixed". You know it's not mixed, since the label is wrong. Say you draw a white ball. You now know that bin is all white balls. You now have two bins left, labeled "black" and "white". The bin labeled "black" cannot be black, so we know that it is mixed; this leaves the bin labeled "white" as mixed.