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Question 80

Let $$A$$, $$B$$, $$C$$ 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 $$C$$ occurs is:

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