The GATE Grind

GATE 2020 EC – Question 22

Communications · Digital Communications · 1 mark · Multiple choice

A digital communication system transmits a block of $N$ bits. The probability of error in decoding a bit is $\alpha$. The error event of each bit is independent of the error events of the other bits. The received block is declared erroneous if at least one of its bits is decoded wrongly. The probability that the received block is erroneous is

  1. $N(1-\alpha)$
  2. $\alpha^N$
  3. $1-\alpha^N$
  4. $1-(1-\alpha)^N$

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Correct answer: (D) $1-(1-\alpha)^N$

Explanation

The block is correct only if all $N$ bits are correct, with probability $(1-\alpha)^N$. So the probability of an erroneous block is $1-(1-\alpha)^N$.