The probability that a single bit will be in error on a typical public telephone line using 4800 bps modem is 10 to the power -3. If no error detection mechanism is used, the residual error rate for a communication line using 9-bit frames is approximately equal to

actual error = error that may happen without any detection mechanism = 0.001
now no detection mechanism is present
so per loss = total_bits_transmitted *probability(error)
loss = 9*0.001=0.009

Here 4800bps is to confuse only,
Probability that single bit is in error = 10^-3 = 0.001
Single bit not in error = 1 - 0.001 = 0.999
Chances that all bits are correct = 0.999^9 = 0.991
Residual error rate = Channel that at least one of 9 bits is incorrect = 1 - 0.991 = 0.009

i want to know the calculation