Question

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.

Answer 1

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`.