The category of cases dealing with situations like that is called "premises liability".
An analysis of a premises liability case starts with determining the status of the injured person as trespasser, licensee, or invitee. The most favorable scenario for a plaintiff is that of a business invitee.
"The possessor of land is liable for injuries to a business visitor caused by a condition encountered on the premises only if he (a) knows or should have known of such condition and that it involved an unreasonable risk; (b) has no reason to believe that the visitor will discover the condition or realize the risk; and (c) fails to make the condition reasonably safe or to warn the visitor so that the latter may avoid the harm." Huston V. Church Of God, 46 Wn. App. 740, 732 P.2d 173 (1987). (You can read relevant cases on the MRSC website.)
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The sign may protect slightly but good housekeeping and current insurance is a better solution. If you have known hazards then you will be liable sign or no sign.
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