  As the only known intelligent civilization, human beings are always curious
about the existence of other communicating extraterrestrial intelligent
civilizations (CETIs). Based on the latest astrophysical information, we carry
out Monte Carlo simulations to estimate the number of possible CETIs within our
Galaxy and the communication probability among them. Two poorly known
parameters have a great impact on the results. One is the probability of life
appearing on terrestrial planets and eventually evolving a into CETI ($f_c$),
and the other determines at what stage of their host star's evolution CETIs
would be born ($F$). In order to ensure the completeness of the simulation, we
consider a variety of combinations of $f_c$ and $F$. Our results indicate that
for optimistic situations (e.g. $F=25\%$ and $f_c=0.1\%$), there could be
$42777_{-369}^{+267}$ CETIs and they need to survive for $3_{-2}^{+17}$ yr
($2000_{-1400}^{+2000}$ yr) to achieve one-way communication (two-way
communication). In this case, human beings need to survive
$0.3_{-0.298}^{+0.6}$ Myr to receive one alien signal. For pessimistic
situations (e.g. $F=75\%$ and $f_c=0.001\%$), only $111_{-17}^{+28}$ CETIs
could be born and they need to survive for $0.8_{-0.796}^{+1.2}$ Myr
($0.9_{-0.88}^{+4.1}$ Myr) to achieve one-way communication (two-way
communication). In this case, human beings need to survive $50_{-49.6}^{+250}$
Myr to receive one signal from other CETIs. Our results may quantitatively
explain why we have not detected any alien signals so far. The uncertainty of
the results has been discussed in detail and would be alleviated with the
further improvement of our astronomical observation ability in the future.
