Question #123909

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

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

Expert's answer

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)}

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