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 $(1-2 k)$, 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

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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 $(1-2 k)$, 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: [JEE Main 2021, 20 Jul (Shift 2)]

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Let \(A, B\) and \(C\) be three events such that the probability that exactly one of \(A\) and \(B\) occurs is \((1-k)\)…

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