I ran the numbers and produced a graph that shows each of the existing candidates and the chance that they will be president of the church in each given year. Graphically, the data looks like this:
(Click on the diagram to zoom in.)
The blue line coming from the upper left shows survival chance of Thomas Monson. You'll notice that not all apostles are equally represented. There's a good chance for Packer, Oaks, Holland and Bednar, each in different years. The other apostles are not nearly as likely to become president. Note that although we can almost rule out some of the candidates, the most likely successors are by no means assured of their place.
The red and blue bell-shaped curves to the left show something rather scary: they represent the possibility of Boyd Packer and Dallin Oaks becoming church presidents. (These two apostles represent the hardest edge of the old guard.)
The following diagram shows the probability that either Packer or Oaks is church president in a given year:
In other words, between 5 and 15 years from now there is an excellent chance that either Elder Packer or Elder Oaks will be president of the church. In fact, there is a lifetime probability of about 70% that eventually at least one of them will take over the presidency.
If you look at the current church leadership, you can divide them into two groups based on age and temperament. The older group (in order of succession) is
Monson (age 82)
Packer (age 85)
Perry (age 87)
Nelson (age 85)
Oaks (age 77)
Ballard (age 80)
Scott (age 80)
Hales (age 77)
The younger, probably more progressive group is lead by Jeffrey Holland:
Holland (age 68)
Eyring (age 76)
Uchtdorf (age 68)
Bednar (age 57)
Cook (age 69)
Christofferson (age 64)
Andersen (age 58)
Since succession in the LDS Church is by strict seniority, it is possible to ask when the church presidents from the older group will be replaced by their younger, more progressive colleagues. The following chart shows the probability of any member of the younger group being president of the church:
Basically, during the next 10 to 15 years the LDS Church will have very conservative leadership, perhaps even more conservative than today. Then, from 10 to 20 years from now there will be a time of transition. Starting 20 years from now, it is very likely that all of the old guard will be gone.
I don't know if these numbers are encouraging or discouraging.
Note on methodology: Ziff's numbers are based on life expectancy data for white males in the U.S. in 2004. I used the same data set as Ziff for the life expectancies, except that I reduced annual mortality [q(x)] by 10 percent across the board to account for the fact that members of the LDS leadership are probably longer lived than the general population.