Let $A, B$ and $C$ be three events such that the probability that exactly one of $A$ and $B$ occurs is $(1-k)$,the probability that exactly one of $B$ and $C$ occurs is $(1-2k)$,the probability that exactly one of $C$ and $A$ occurs is $(1-k)$ and the probability that all $A, B$ and $C$ occur simultaneously is $k^2$,where $0 < k < 1$. Then the probability that at least one of $A, B$ and $C$ occurs is:

• A
  greater than $\frac{1}{2}$
• B
  greater than $\frac{1}{4}$ but less than $\frac{1}{2}$
• C
  exactly equal to $\frac{1}{2}$
• D
  greater than $\frac{1}{8}$ but less than $\frac{1}{4}$