Sanjay writes a letter to his friend from IIT, Kanpur. It is known that one out of ‘n’ letters that areposted does not reach its destination. If Sanjay does not receive the reply to his letter, then what isthe probability that Kesari did not receive Sanjay’s letter? It is certain that Kesari will definitelyreply to Sanjay’s letter if he receives it.
Answers
Given : Sanjay writes a letter to his friend from IIT, Kanpur.
It is known that one out of ‘n’ letters that are posted does not reach its destination.
It is certain that Kesari will definitely reply to Sanjay’s letter if he receives it.
To Find : If Sanjay does not receive the reply to his letter, then what is the probability that Kesari did not receive Sanjay’s letter?
Solution:
Sanjay writes a letter to his friend Kesari
Probability that Kesari Does not receive letter =1/n
in that case probability that Sanjay did not receive Kesri reply = 1/n
Probability that Kesari receive letter = (n - 1)/n
probability that Sanjay did not receive Kesri reply = (n-1)/n * 1/n
= (n - 1)/n²
probability that Sanjay did not receive Kesri reply = 1/n + (n - 1)/n²
If Sanjay does not receive the reply to his letter, then what is the probability that Kesari did not receive Sanjay’s letter
= 1/n / ( 1/n + (n - 1)/n²)
= n/(n + n - 1))
= n/(2n - 1)
n/(2n - 1) is the probability that Kesari did not receive Sanjay’s letter If Sanjay does not receive the reply to his letter
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