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dalvyx [7]
3 years ago
5

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.
Mathematics
1 answer:
Artyom0805 [142]3 years ago
6 0

Answer:

The probability of the defendant is innocent given the defendant is convicted is P=0.006.

Step-by-step explanation:

Being:

G: guilty, I:innocent, C: convicted, A: acquitted.

We need to calculate P(I|C).

Being innocent, given convicted, is equal to the probability of being innocent and convicted divided by the probability of being convicted (innocent or guilty)

P(I|C)=\frac{P(I\&C)}{P(C)}

The probability of being innocent and convicted is

P(I\&C)=P(C|I)*P(I)=0.05*0.1=0.005

The probability of being convicted is equal to the sum of P(I&C) and P(G&C)

P(C)=P(I\&C)+P(I\&C)=P(C|I)*P(I)+P(C|G)*P(G)\\\\P(C)=0.005+0.95*0.90=0.005+0.855=0.86

Then,

P(I|C)=\frac{P(I\&C)}{P(C)}=\frac{0.005}{0.86}= 0.006

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