A digital communications system consists of a transmitter and a reciever. During each short transmission interval the transmitter sends a signal which is to be interpreted by a zero, or it sends a different signal which is to be interpreted as a one. At the end of each interval the reciver makes the best guess at that was transmitted. Consider the events:

T0 = {Transmitter sends 0}

T1 = {Transmitter sends 1}

R0 = {Receiver concludes that a 0 was sent}

R1 = {Reciever concludes that a 1 was sent}

Assume that P(R0|T0) = 0.99, P(R1|T1) = 0.98 and P(T1) = 0.5

Find

a) the probability of a transmission error given R1?

b) the overall probability of a transmission error

c) repeat a) and b) assuming P(T1) = 0.8 instead of 0.5