Question

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. Compute the probability that the sender sends exactly

n packets until the receiver can decode the message successfully

Answer 1

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.

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

Therefore,

Required probability = nCk * (p)^k * (1-p)^(n-k)