What is the probability of ...

[lepelke4]

When the jailor dies to the serial killer in the first night, the probability that the jailed person is the serial killer is 51.8%.
When the jailor dies to the serial killer in the first night and the death note has the jailor's name, the probability that the jailed person is the serial killer is 7.1%.

This assumes that the sk has no way of knowing the jailor's name.

Define the events
A = jailor died to sk
B = sk was jailed
C = sk got the jailor's name in death note

Now it is just a straightforward application of conditional probabilities:
P(B|A) = P(A and B) / P(A) = P(A and B) / [ P(A|B)P(B) + P(A|not B)P(not B) ] = 1/14 / [1/14 + 1/14 13/14] = 1 / [1 + 13/14] ≈ 51.8%
P(B|A and C) = P(A and B and C) / P(A and C) = P(C|B)P(B) / [ P(A and C|B)P(B) + P(A and C|not B)P(not B) ] = 1/14 * 1/14 / [1/14 * 1/14 + 1/14 * 13/14] = 1/14 ≈ 7.1%

update: apparently there is a bug that allows you to change your death note AFTER the day starts. If there are two dead bodies at the start of the day, and the sk manages to update his death note to mention one of them, that increases the second probability to 35%.

[SantanaTheSmall]

I love this kind of post, thank you. Reminds me of playing as invest before the new role list and using math to make certain decisions.

Like, if you found BG, GF, Arso, it was more probable that the person was GF instead of BG and NOT 50/50 like some smooth brained sod tried to tell me.

There’s much less of that with the new invest results and role list.

[Joacgroso]

I know this has nothing to do with the OP, but does anyone know what are the chances of a juggernaut spawning?