A telecommunications system transmits binary signals (0 or 1). The system includes a transmitter that emits the signals and a receiver which receives those signals. The probability that the receiver registers a signal 1 when the transmitter has sent a signal 1 is 99.5%, while the probability that the receiver registers a signal 0 when the transmitter has sent a signal 0 is 98%. Signals are transmitted every second, and so 60 signals are sent during one minute. If the last signal has been registered as 1, find the probability that the original signal transmitted was also 1, if it is known that

(a) equal numbers of 0’s and 1’s are transmitted every minute;

(b) the number of 0’s transmitted during a minute is four times the number of 1’s.