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GATE ECE 2008 | Question-67

Consider a Binary Symmetric Channel (BSC) with probability of error being $p$. To transmit a bit, say $1,$ we transmit a sequence of three $1s.$ The receiver will interpret the received sequence to represent $1$ if at least two bits are $1.$ The probability that the transmitted bit will be received in error is

  1. $p^{3}+3 p^{2}(1-p)$
  2. $p^{3}$
  3. $(1-p)^{3}$
  4. $p^{3}+p^{2}(1-p)$
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