Death Penalty and False Positives

[Fear_of_Math]

Discussing wheather to convict someone charged with murder and give them the death penalty, consider the variables "reality (defendant guilty, defendant innocent) and "decision" (convict, acquit)

Jurors are asked to convict a defendant if they feel the defendant is "guilty beyond reasonable doubt" Suppose this means given the defendant is executed, the probability that s/he is truly guilty is 0.99. For the 873 people put to death from 1977 until September 2003, find the probability that:

i) they were all truly guilty

ii) at least on of them was actually innocent

[Fear_of_Math]

Okay, is P(all those executed were actually guilty)= 0.99^873?
P(at least one innocent)= 0.01^873

Anyone who can let me know if I'm on the right track is appreciated =)

[Random Variable]

0.01^873 is the probability that they're all innocent

P(at least one of them is innocent) = 1 - P(all 873 are guilty)