So let's break this down:
The probability is incorrect, sayeth the actuary. The mortality table they're using is for life insurance, which has conservatism built in.
If you have Excel, you can download my spreadsheet and try it out for yourself.
I put in 72-year-old male. Now I use two different mortality tables, and they're for different purposes. One mortality table (giving the lower life expectancy) is the general Social Security calendar year 2000 table. This is the general population mortality for the U.S. in the year 2000. Life expectancy for a 72-year-old man is about 11.4 years. Now that's the average but not the survival probability. You'll notice that the least number of years that will display is 10 years for the 72-year-old man. Click on the "Change mortality tables" button a couple times. Then stop it on the Social Security mortality table. You'll see it in small print at the bottom of the results area.
I wrote this spreadsheet, but I welcome you to walk through the guts with me. Go to Tools > Protect > Unprotect Workbook (I don't password protect, but protect to keep people from doing stupid stuff). Now go to Tools > Options ... > View tab and click on Sheet tabs. Now go to Format > Unhide sheet... > and choose the "Calcs" sheet.
Let's look on the calcs sheet. Column C, labeled S(x), is the survival probability. So C5 shows 1 as the guy is 72 (age is in column A) and obviously has survived to age 72. We need McCain to survive to age 77 to get all the way through one term (I don't want to deal with fractional age issues, so let's pick the more conservative) and to age 81 to get through two terms.
With the SS CY 2000 table, the probability of surviving one term is almost 80% and two terms is about 60.5%.
So what is this "32% chance of survival" stuff? They're using life insurance tables. There's a problem with life insurance tables -- we build in conservatism in assuming you'll die earlier than expected, because that's where the companies will get hurt if you buy life insurance. The only underwriting variable I have is his age and sex, and a few details of his cancer history. I could try to make an adjustment off the Social Security tables, but they weren't set up for that.
Now, I claim the SS CY 2000 table is still pretty conservative, because it covers everyone, from the extremely fit and active to the highly disabled and chronically ill. McCain has been pretty active, and his mother is still alive, so I would guess his "mortality table" (if there were such a thing) would be better than the population in general. Which makes me want to go to the other mortality table.
The purpose of the life expectancy calculator I wrote is to help people plan for retirement, as many people might not have a good concept of how long they could live if they've survived up to age 65 (or in McCain's case, 72.) First, people hear about life expectancy from birth, but that's irrelevant if you've survived many years past birth. Life expectancy from birth averages in the people who died at age 15 as well as those who died at age 85. You have to calculate the probabilities starting at current age.
The second problem is, you can't go by when your parents or grandparents died alone as there have been =huge= improvements in mortality rates, given a huge drop in smoking rates (much more for men than women) as well as improved safety (fewer accidental deaths) and health (better survival rates for cancer and heart disease). To be sure, obesity militates against improvement, but so far it's been steady improvement over the last 100 years .... and I've seen evidence of accelerated improvement in the senior ages in the last ten years. We're getting a little far afield, so check this out for light reading.
Anyway, let's pull up the annuitant mortality table. Go back to the front page, change mortality tables to the SOA A-2000 table.
Survival probabilities for 72-year-old man:
to age 77: 87.7%
to age 81: 74.5%
Now, given McCain's cancer status, it may not be appropriate to use this table, but given the level of healthcare he has access to, and his long-lived mother, and his general health status aside from the cancer, it might not be too bad. Say this is the upper range for survival probabilities.
So what does this mean in practicality? Not much, frankly. The central limit theorem doesn't kick in at one person. I'm just trying to do a little education here. If we want to go with the stats of people dying in office, only a few had "natural" deaths (having read about FDR's health stats... wooo... it's amazing he lived that long. Top number for blood pressure around 300!) - assassins have held far more danger than old age. Remember it was John Hinckley who almost did in Reagan, not his old age -- and even his Alzheimer's disease didn't claim him until a few years ago.
There are also morbidity tables to go for possibilities of various incapacitating conditions that would require McCain to resign, but it's really not that useful to look at.
Considering the number of well-known people who suddenly died this year, many of whom were around twenty years younger than McCain, anybody can pop off at any time. Teddy Roosevelt was expected just to be a placeholder, and his VP pick was to stop him messing around with the NY political machine. Well, we see where that led. So I am not trying to diminish the risks here. I'm just trying to get the order of magnitude into the correct range.
UPDATE: I just found a pretty good article on this, with good numbers, and quoting some people I know. Jim Daniel and Jack Luff most definitely know what they're talking about. They are using more up-to-date mortality tables, too. I need to deal with that in my calculator.