Signal transmission probability

[mattc]

In the digital signal transmission, due to noise, the received signals may be different from the signals sent out. Suppose the transmitter sends out signal 0 with probability 0.7, and 1 with probability 0.3. When 0 is transmitted, the receiver receives 0 with probability 0.8, and 1 with probability 0.2. When 1 is
transmitted, the receiver receives 0 with probability 0.1, and 1 with probability 0.9. Find the probability of error, i.e. the probability that 1 is received when 0 was transmitted or 0 is received when 1 was transmitted.

[quark]

P(0 transmitted)=0.7
P(1 transmitted)=0.3
P(0 received | 0 transmitted)=0.8
P(1 received | 0 transmitted)=0.2
P(0 received | 1 transmitted)=0.1
P(1 received | 1 transmitted)=0.9

P(error)=P(1 received | 0 transmitted)*P(0 transmitted) + P(0 received | 1 transmitted)*P(1 transmitted)
=0.2*0.7 + 0.1*0.3
=0.17