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Question: It is known that one out of 'n' letters doesn't reach its destination. I write a letter to my friend...

It is known that one out of 'n' letters doesn't reach its destination. I write a letter to my friend and don't get reply.

Had my friend received my letter, certainly he would have

replied. Find the probability that my friend received my letter.

A

B

n+12n−1\frac { n + 1 } { 2 n - 1 }

C

D

Answer

Explanation

Solution

Let A and B be the events of my letter reaching and not

reaching my friend respectively.

P(1) = n−1n\frac { \mathrm { n } - 1 } { \mathrm { n } } , P(2) = 1n\frac { 1 } { \mathrm { n } } .

Let E be the event that I don't get reply

P(E/A) = P(E/B) = 1

P(A/E) = n−1n×1nn−1n2+1n×nn=n−1n−1+n=n−12n−1\frac { \frac { n - 1 } { n } \times \frac { 1 } { n } } { \frac { n - 1 } { n ^ { 2 } } + \frac { 1 } { n } \times \frac { n } { n } } = \frac { n - 1 } { n - 1 + n } = \frac { n - 1 } { 2 n - 1 } .