In a classification problem involving three classes with prior probabilities p$1,$ p$2$ and p$3($p$1,$ p$2,$ p$>0),$ if the Bayes risk is $\{1(($p$1)^2+($p$2)^2+($p$3)^2)\},$ which of the following statement is $**$false$**.(1)$ or $(2)?$ Please provide a detailed explanation.

$(1)$ Bayes classifier is as good as the random classifier which randomly assigns observations to one of the three$$ classes.

$(2)$ All competing classes have identical distribution.