Prof. Ankush writes a research paper on availability of internet and other related services in rural areas. He wants to share his research with Prof Kannu. There is a small bottleneck. He is in a remote area. Letters are only medium of communication. So, he writes a letter to his friend. The postal department tells him that on an average, 1 out of n letters posted does not reach it’s desired location. Now, if Ankush doesn’t receive the reply to his letter, then what is the probability that Kannu did not receive Ankush’s letter. You can safely assume that postal services are perfect at Kannu’s residence and he will definitely reply to Ankush’s letter if he receives it.
Answers
Given : Prof. Ankush writes a research paper , he send letter to Prof kannu. The postal department tells him that on an average, 1 out of n letters posted does not reach it’s desired location.
To find : if Ankush doesn’t receive the reply to his letter, then what is the probability that Kannu did not receive Ankush’s letter.
Solution:
Probability of letter not reaching to kannu = 1/n
Probability of letter reaching to kannu = (n -1)/n
Probability that ankush Does not receive reply =
kannu not receiving + kannu letter not reached to ankush
= 1/n + ((n-1)/n)(1/n)
= (n + n - 1 )/n²
= (2n - 1)/n²
probability that Kannu did not receive Ankush’s letter. = (1/n)/((2n - 1)/n²)
= n/(2n-1)
n/(2n-1) is the probability that Kannu did not receive Ankush’s letter.
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