Question

You’re a jury member for Smith who’s being tried for murder. On the basis of everything you’ve heard so far, you put the probability that Smith did it at .65. Today, an eyewitness, who you think is .7 reliable, said that Smith did not commit the crime. Now what is the probability of Smith’s guilt?

Answer 1

From everything that you hreard so far the probability of Smith committed the murder is

= 0.65

Now the eye witness is saying that Smith did not commit the murder.

The probability that the man is saying truth is = 0.7 and the man is saying lie is = 1-0.7=0.3

So now only case that can conclude that Smith committed the crime is All the things i heard is true and th witness is telling lie.

Then the probability of smith is guilty is

= Probability of everything i heard is true × probability of the man is telling lie

= 0.65 × 0.3

= 0.195