Hint
The probability that there is a replacement event in a time interval of width $\Delta t$ is the product of probability of
- the probability per day that a given individual is replaced,
- the number of individuals, and
- the length of the time interval (measured in days to match the probability per day, but we're not worrying about that detail).
To obtain the probability that $N$ increases by 1 during the time interval, you simply need to multiply this product by the probability that any given replacement event increases the number of $A$ alleles by 1, which you just calculated.
Hide help