Using the repetition code, you have a three$-$bit string that encodes a logical bit.

a$.$ If the parity of the left two bits is odd, and the parity of the right two bits is also odd, has

a single$-$bit error occurred? If yes, which bit was flipped $($the left, middle, or right bit$)?$

b$.$ If the parity of the left two bits is odd, but the parity of the right two bits is even, has a

single$-$bit error occurred? If yes, which bit was flipped $($the left, middle, or right bit$)?$

c$.$ If the probability of a single bit flipping is $p=0\mathrm{.}2,$ what is the probability that an

uncorrectable error occurs with the $3-$bit repetition code? In this case, does the $3-$bit

repetition code increase or decrease the probability of an uncorrectable error occurring?

d$.$ If the probability of a single bit flipping is $p=0\mathrm{.}7,$ what is the probability that an

uncorrectable error occurs with the $3-$bit repetition code? In this case, does the $3-$bit

repetition code increase or decrease the probability of an uncorrectable error occurring?