In a jury trial, suppose the probability the defendant is convicted, given guilt, is 0.95, and the probability the defendant is acquitted, given innocence, is 0.95. suppose that 90% of all defendants truly are guilty. find the probability the defendant was actually innocent given the defendant is convicted.

These are the following events: guilty = g,innocent = i,acquitted = a,convicted = cfrom the problem we get the following values: p(g) = 0.9, p(i) = 0.1 p(c | g) = 0.95p(a | g) = 0.05 p(a | i) = 0.95,p(c | i) = 0.05therefore, p(i and c) = p(c | i)*p(i) = 0.05*0.1 = 0.005p(c) = p(g and c) = p(i and c)= (0.95)*(0.9) + ( 0.05)*(0.1)= 0.855 + 0.005 = 0.86so p(i | c) = p(i and c) / p(c) = 0.005/0.86 = 0.00

The answer to your question is the last one