Question

A truth serum given to a suspect is known to be 90% reliable when the person is guilty and 96% reliable when the person is innocent. In other words, 10% of the guilty are judged innocent by the serum and 4% of the innocent are judged guilty. Suppose that a suspect was selected from a group of suspects of which only 4% are guilty of having committed a crime. If the serum indicates that the suspect is guilty of having committed a crime, what is the probability that the suspect is innocent? (Round your answer to 3 decimal places.) Suggestion: Use a probability tree for this calculation. Probability

Answer 1

Answer :

given data :-

Let A be the occasion that the suspect is blameworthy of the wrongdoing.

We are given P(A) = 4%

= 4/100

= 0.04

so likelihood of the suspect isn't liable of the wrongdoing,

P(B) = 1 - 0.04

= 0.96

Give B a chance to be the occasion that the serum uncovers that the suspect is blameworthy.

We are given that P(B | A) = 90

= 90/100

= 0.90

So P( | A) = 1 - 0.90

= 0.10

and

P( | ) = 96%

= 96/100

= 0.96

so P(B | ) = 1 - 0.96

= 0.04

P(A B) = 4%

= 4/100

= 0.04

The complete likelihood recipe says P(B) = P( B) + P(A B)

= P() P(B | ) + P(A)P(B|A)

= 0.96 * 0.04 + 0.04 * 0.90

= 0.038+0.036

= 0.074

We are approached to register

P( | B) = P( B)/P(B)

= P() P(B | )/P(B)

= 0.96 * 0.04/0.074

= 0.96*0.540

= 0.518

the probability that the suspect is innocent is = 0.518