Is it legal for employers to RANDOMLY search employee purses, briefcases, etc?

Last week my employer sent around a memo that is supposed to be revised, but currently states that they "reserve the right to examine all packages, handbags, or brief cases in possession of any ociates entering or leaving the property". This has everyone infuriated, and wondering about the legality. The search is supposed to be random, meaning they would not have probable cause or anything. I know that stores cannot search personal articles, law enforcement must be present, is it the same for employers?