Consider a Binary Symmetric Channel (BSC) with probability of error being $p$. To transmit a bit, say $1,$ we transmit a sequence of three $1\text{s}.$ 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
- $p^{3}+3 p^{2}(1-p)$
- $p^{3}$
- $(1-p)^{3}$
- $p^{3}+p^{2}(1-p)$