In many cases in networks, instead of using all 8 bits for data, we often utilize only 7 bits for data and one bit for control. Specifically, this control | bit is an even-parity bit to ensure that the number of bit 1 in total 8 bits-long data is always even. Assume a binary symmetric channel with bit error probability Pe as in the lecture note. All bit errors are independent of another. Sender A now transmits an 8-bit long packet (7 data bits + one even-parity bit) onto this binary symmetric channel. The receiver B receives a packet and there are total three possibilities: Case 1: no bit has been inverted (no error) so the receiver successfully receives the packet. Case 2: Some bits are inverted (error!) and the receiver can correctly detect the error. Case 3: Some bits are inverted (error!) but the receiver mistakenly concludes that the packet is (or appears to be) error-free. Find the probability of each of these three cases. No need to find a closed form. Just leave your expresSIOn as IS