Calculate the odds that a given name should have the first and last names swapped? I have a personal project I'm working on and could use some help with the math. Let's say I had two lists. 
FN: 1 million first names (dupes allowed).
LN: 2 million last names (dupes allowed).
And let's say we're looking at two names:
"Murray": Appears in FN 5,000 times and in LN 75,000 times.
"Harrison": Appears in FN 10,000 times and in LN 70,000 times.
I'm given "Murray Harrison" as a full name. How would you approach calculating the odds that the intended name was actually "Harrison Murray"? For the scope of this project, it is acceptable to assume that any last name is just as likely to appear next to any first name.
I think that:
P(Murray Harrison) = P(Murray as First) * P(Harrison as Last) = 5000/80000 * 70000/80000 = 0.055
P(Harrison Murray) = P(Harrison as First) * P(Murray as Last) = 75000/80000 * 10000/80000 = 0.117
Here's where my question might get tricky:
How would you take those two probabilities and determine the odds that the two names should be swapped? For example, say I decide that if there's a 95% chance they should be swapped, I'll swap them.
Would I need additional data to determine this probability? Would I just look at the probabilities of both name orders and if one's > 0.95 I would select that order?
Edit: To be clear, I have a list of full names and I want to programmatically determine which name is the first name, and which is the last. Sometimes the data will be in Last-First order (without a comma) and sometimes it will be in First-Last order. I'm trying to use a bit of stats to determine the most likely order.
 A: I have doubts about your assumption that any first name can appear next to any last name. In the real world there is a strong dependence. Drawing "Itzhak" or "Yo Yo" from the first names list would drastically alter the real distribution of the last names. It would be better to have a large list of full names. If you find two Murray Harrisons and no Harrison Murrays, that's stronger evidence. Nevertheless, let's continue with your independence assumption:
If your hypothesis is that the name under test is reversed, then your odds of the hypothesis given a particular name is
$$Odds(reversed|name) = Odds(reversed) \frac{P(name|reversed)}{P(name|correct)}$$
The likelihood of drawing "Murray Harrison" from your lists is 0.005 * 0.035 = 0.000175 and the likelihood of drawing "Harrison Murray" is 0.01 * 0.0375 = 0.000375. Your likelihood ratio increases the odds of the reversed hypothesis by a factor of 2.143. This is pretty weak evidence. Your prior odds of any given name being reversed would have to be almost 9:1 to meet your P > 0.95 threshold. 
