Problem 18 In a communication system packets are transmitted

Problem 18 In a communication system, packets are transmitted from a sender to a receiver. Each packet is received with no error with probability p independently from other packets (with probability 1 -p the packet is lost). The receiver can decode the message as soon as it receives k packets with no error. Find the probability that the sender sends exactly n packets until the receiver can decode the message successfully.

Solution

In the case where the receiver decode as soon as possible , the packets receiver by him without error must exactly be k out of n packets.

Also , only two possibilities are there i.e Success or Failure , it behaves like a binomial probability.

Hence,

Desired Probability = nCk * (p)^k * (1-p)^(n-k) Answer