In Hamming code we require 10 parity bits

$2^P\geq P+M+1$ where M=1000

In Hamming code we require only one transmission (this is Forward Error Correcting Code). on detection of 1 bit error the receiver will try to guess the correct message

So we're transmitting 1010 bits per block basis(message bits+redundant bits)

in case of error detection and retransmission let the error rate be x per bit i.e. probability that a bit got corrupted=x

in error detection and retransmission, we transmitting 1001 bits per block basis(1000+1 parity bit)

for a block of 1000 bits there could be 1000x bit errors

for example if x=0 i.e. probability of a bit getting corrupted is nil, there there will be no retransmission required

If x=0.1 so in a block 0.1*1000=100 bits are inverted so there will be 100 retransmissions+1 beginning transmission. And we've to transmit 1001+100*1001 bits

if x=1 then 1*1000 all bits are inverted and there will be 1000 retransmissions of 1001 bits

for every bit error in a block 1001 bits will be retransmitted. so there will be 1000x*1001 bit retransmission+1 transmission of 1001 bits in the beginning

so we're transmitting 1001+1000x*1001 bits

if error detection and correction is better than Hamming code then

1001+100x*1001 < 1010

x<$9*10^{-6}$ approx

Thus, a bit should have less than $9*10^{-6}$ probability of getting inverted