Someone help me with some proability...

[Jubal_Barca]

Hit scum, 2/8, SK hits town, 5/6,
Hit scum, 2/8, SK hits scum, 1/6
Hit town, 5/8, SK hits town, 5/6
Hit town, 5/8, SK hits scum, 2/6
Hit SK, 1/8, ...,

Ok, this is from a game of Mafia. 8 players, 2 scum, 5 town, 1 SK.

In the day all the players lynch, at night the SK sends in a choice of one player to kill, assuming the SK is still alive.

From the above data, I need to know the probabilities (as fractions preferably) of;
2 town dying
1 town and 1 scum dying
2 scum sying
The SK dying

I'm struggling with this... if anyone can help +rep.

[Simetrical]

Does the day go first here or the night? If, say, the day goes first, you can break it down by possibilities:

1. Two scum die: first the town must hit a scum (2/8), then the serial killer must (1/6). Total probability: 2/48.
2. Two town die: first the town must hit a town (5/8), then the serial killer must (4/6). Total probability: 20/48.
3. Serial killer dies: easy, 1/8 (= 6/48).
4. One town and one scum: two possibilities. Either the town hits a town (5/8) and the SK hits a scum (2/6) = 10/48; or the town hits a scum (2/8) and the SK hits a town (5/6) = 10/48. Total probability is 20/48.

It breaks down a bit differently if the SK is going first (although rereading your post, I gather that's wrong):

1. Two scum die: first the SK must hit a scum (2/7), then the town must (1/7). Total probability: 2/49.
2. Two town die: first the SK must hit a town (5/7), then the town must (4/7). 20/49.
3. Serial killer dies: easy again, flat 1/7 = 7/49. (It makes no difference who the SK kills.)
4. One town and one scum: two possibilities again. SK hits town (5/7) then town hits scum (2/7) = 10/49, or SK hits scum (2/7) then town hits town (5/7) = 10/49. Total is 20/49.

(Interestingly, the only difference between the two scenarios is slightly raising the chance of an SK kill at the expense of others. The SK is more vulnerable in the second scenario since he's knocked off a suspect. As this illustrates, the best way for mafia or SK to delay dying, on purely probabilistic grounds, is to not kill anyone ― although this probably won't help their long-term chances, I haven't calculated.)

All this assumes that the town's vote is going to be random, which of course it won't be.