If you\'re having difficulty with this question, please view this video to see a

Question

If you're having difficulty with this question, please view this video to see a similar example. 1. Suppose jurors make the right decisions about guilt and innocence 75% of the time and that 50% of all defendants are truly guilty. Fill in the table below for 100 defendants. 2. what is the chance of a convicted defendant truly being innocent? Write your answer as a fraction, not a % 3. What is the chance of an convicted defendant truly being innocent? Now write your answer as a percentage, but don't include % sign. 4. What is the chance of an acquitted defendant truly being guilty? Write your answer as a fraction, not a %. 5. What is the chance of an acquitted defendant truly being guilty? Now write your answer as a percentage, but don't include % sign.

Explanation / Answer

Let I shows the event that defendant is innocent and G shows the event that defendant is guilty. So we have

P(I)= 0.50 and P(G) = 0.50

Let A shows the event that defendant is acquitted and C shows the event that defendant is convicted. So we have

P(A|I) = 0.75

P(C|G) = 0.75

So

P(A and I) =P(A|I) P(I) = 0.75 *0.50 = 0.375

P(C and G) =P(C|G) P(G) = 0.75 *0.50 = 0.375

Following is the completed table:

2.

Here we need to find the probabaility P(I|C).

P(I and C) =12.5 /100 =0.125

P(C) = 50 /100 =0.50

So required probabaility is

P(I|C) = P(I and C) / P(C) = 0.125 / 0.50 = 1 / 4 = 0.25

3.

P(I|C) = P(I and C) / P(C) = 0.125 / 0.50 = 1 / 4 = 0.25 = 25%

4.

Here we need to find the probabaility P(G|A).

P(G and A) =12.5 /100 =0.125

P(A) = 50 /100

P(G|A) = P(G and A) / P(A) =  0.125 / 0.50 = 1 / 4 = 0.25

5.

P(G|A) = P(G and A) / P(A) =  0.125 / 0.50 = 1 / 4 = 0.25 = 25%

Acquitted Convicted Innocent 0.375*100=37.5 50-37.5=12.5 50 Guilty 50-37.5=12.5 0.375*100=37.5 50 Total 50 50 100

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