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okay so there is a group of inmates: 5% are guilty and 95% are innocent

a truth serum is being used; when used on guilty inmates, it has a 90% chance of working (causing them to end up guilty) and a 10% chance of failure (causing them to end up innocent). when used on innocent inmates, it has a 99% chance of working (resulting in innocent) and a 1% chance of failure (resulting in guilty).

I need to find the probability of an inmate being guilty if the serum's result is innocent, as well as vice-versa, but that should be trivial once I figure out how to do the first one.

I drew a tree thing but it's not really helping me:

http://img27.imageshack.us/img27/7988/treefsy.jpg [Broken]

is the first one (.005) / (.005 + .9405)?

a truth serum is being used; when used on guilty inmates, it has a 90% chance of working (causing them to end up guilty) and a 10% chance of failure (causing them to end up innocent). when used on innocent inmates, it has a 99% chance of working (resulting in innocent) and a 1% chance of failure (resulting in guilty).

I need to find the probability of an inmate being guilty if the serum's result is innocent, as well as vice-versa, but that should be trivial once I figure out how to do the first one.

I drew a tree thing but it's not really helping me:

http://img27.imageshack.us/img27/7988/treefsy.jpg [Broken]

is the first one (.005) / (.005 + .9405)?

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