In the wake of Senator McCain selecting Gov. Palin to be his running mate, many words have been devoted to the possibility of Sen. Biden or Gov. Palin unexpectedly becoming President. However, I have seen no discussion of the probability of this actually happening.
Our nation’s history provides us with a sample of 42 Presidents and 46 Vice-Presidents (including Bush and Cheney) from which we can estimate this probability. The number of Presidents and Vice-Presidents is unequal because Presidents have had between zero and three Vice-Presidents. Eight VPs have become President upon the previous President’s death (most recently Johnson), and one VP has become president upon the President’s resignation (Ford).
So, the probability of our next VP unexpectedly becoming President is
I am not sure how to do error propagation on a calculation like this.