GATE Electronics and Communications (EC) 2020 Solved Papers

Question : 19 of 65

Marks: +1, -0

A digital communication system transmits a block of

{N}

bits. The probability of error in decoding a bit is a a. The error event of each bit is independent of error events of other bits. The received block is declared erroneous if at least one of the bits is decoded wrongly. The probability that the received block is erroneous is

$N(1-a)$
$1- {a}^{ {N}}$
${a}^{ {N}}$
$1-(1-a)^{N}$

Validate

Solution:

error probability

=a

correct probability

=1-a

'N' Bits So
Correct probability

=(1-a)(1-a) . . . ⋅^{'} N^{'}

times

=(1-a)^{N}

Erroneous probability

=1

- correct probability

=[1-(1-a)^{N}]

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