Problem 34P

In Example 3f, suppose that the new evidence is subject to different possible interpretations and in fact shows only that it is 90 percent likely that the criminal possesses the characteristic in question. In this case, how likely would it be that the suspect is guilty (assuming, as before, that he has the characteristic)?

Solution :

Step 1 of 1:

Our goal is :

Now we need to find how likely would it be that the suspect is guilty.

Let G denotes the event that the suspect is guilty.

Then the probability of the guilt of a certain suspect is

0.6

Then is

1-0.6

0.4

Given the new evidence is subject to different possible interpretations and in fact shows only that it is 90 percent.

Let C denotes the event that he posses the characteristic of the criminal.

So G is already happening event.

Then the probability of C given G is

0.9

Therefore, the probability of C given G is 0.9.

Now we have to compute .

Here is

Where,

1-0.9

0.2 and

1-0.6

0.4

0.8709

Therefore, is 0.8709.