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 = C

From the problem we get the following values:

P (G) = 0.9, P (I) = 0.1 P (C | G) = 0.95

P (A | G) = 0.05 P (A | I) = 0.95,

P (C | I) = 0.05

Therefore, P (I and C) = P (C | I) * P (I) = 0.05*0.1 = 0.005

P (C) = P (G and C) = P (I and C) = (0.95) * (0.9) + (0.05) * (0.1)

= 0.855 + 0.005 = 0.86

So P (I | C) = P (I and C) / P (C) = 0.005/0.86 = 0.00