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 of 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 $C$ occur is: (1) greater than $\frac { 1 } { 8 }$ but less than $\frac { 1 } { 4 }$ (2) greater than $\frac { 1 } { 2 }$ (3) greater than $\frac { 1 } { 4 }$ but less than $\frac { 1 } { 2 }$ (4) exactly equal to $\frac { 1 } { 2 }$
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 of 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 $C$ occur is:\\
(1) greater than $\frac { 1 } { 8 }$ but less than $\frac { 1 } { 4 }$\\
(2) greater than $\frac { 1 } { 2 }$\\
(3) greater than $\frac { 1 } { 4 }$ but less than $\frac { 1 } { 2 }$\\
(4) exactly equal to $\frac { 1 } { 2 }$