A digital communications system consists of transmitter and a receiver. During each short transmission interval the transmitter sends a signal which is to be interpreted as A zero, or it sends a different signal which is to be interpreted as a one. At the end of each interval, the receiver makes its best guess at what was transmitted.
Consider the events:
$T_0$ = {transmitter sends 0}, $R_0$ = {receiver concludes that a 0 was sent}
$T_1$ = {transmitter sends 1}, $R_1$ = {receiver concludes that a 1 was sent}
Assume that: $\mathsf P(R_0\mid T_0)=0.99,\\ \mathsf P(R_1\mid T_1)=0.98,\\ \mathsf P(T_1)=0.5$
Find:
(a) the probability of A transmission error given $R_1$;
(b) the overall probability of a transmission error;
(c) Repeat (a) and (b) assuming $\mathsf P(T_1)=0.8$ instead of $0.5$
To get you started
Find: $\mathsf P(T_0\mid R_1)$
Find: $\mathsf P((T_1\cap R_0) \cup (T_0\cap R_1))$