State whether each of the following statements is true or false:
$(1)$ For the probability $P(A)$ of any event $A$,$0 < P(A) < 1$.
$(2)$ The probability of the month of March having $5$ Sundays is $\frac{1}{7}$.
$(3)$ If the probability of an event $A$ occurring is $\frac{3}{7}$,then the probability of event $A$ not occurring is $\frac{4}{7}$.

(C) $(1)$ False. The probability $P(A)$ of any event $A$ satisfies $0 \le P(A) \le 1$. It can be $0$ (impossible event) or $1$ (sure event).
$(2)$ False. March has $31$ days,which means $4$ weeks and $3$ extra days. The extra days can be (Sun,Mon,Tue),(Mon,Tue,Wed),(Tue,Wed,Thu),(Wed,Thu,Fri),(Thu,Fri,Sat),(Fri,Sat,Sun),or (Sat,Sun,Mon). Out of $7$ possibilities,$3$ contain a Sunday. Thus,the probability is $\frac{3}{7}$.
$(3)$ True. The probability of an event not occurring is $P(\text{not } A) = 1 - P(A)$. Given $P(A) = \frac{3}{7}$,then $P(\text{not } A) = 1 - \frac{3}{7} = \frac{4}{7}$.