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Ramesh appears for an interview for two posts, A and B, for selection is independent. The probability for his selection for Post A1/6) and for Post B, it is (1/7). Find the probability that Ramesh is selected for at least one post. Select the correct answer from above options

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Let `E_(1) =` event that Ramesh is selected for the post A, and `E_(2) =` event that Ramesh is selected for the post B. Then, `P(E_(1))=1/6` and `P(E_(2))=1/7`. Clearly, `E_(1)` and `E_(2)` are independent events. `:. P(E_(1) nn E_(2))=P(E_(1))xxP(E_(2))=(1/6xx1/7)=1/42`. `:.` P(Ramesh is selected for at least one post) `=P(E_(1) uu E_(2))` `=P(E_(1))+P_(E_(2))-P(E_(1) nn E_(2))` `=(1/6+1/7-1/42)=12/42=2/7`. Hence, the required probability is `2/7`.

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