1. ## probability

Suppose that 100 people were arrested and each is given a polygraph test. It is known that the polygraph is 92% reliable when given to someone who is guilty, and 95% reliable when given to someone who is innocent. Suppose that only 10 out of the 100 people were actually involved in any wrongdoing. Find the probability that the polygraph test says that a given suspect is guilty.

2. $p(Guilty) = 10/100 = 1/10$
$p(Innocent)= 1- 1/10 = 9/10$

Now,

$P(Detects|G) = .92$
$P(D|I) = .95$

$P(D) = P(D|G)P(G) + P(D|I)P(I) = .92 \times 1/10 + .95 \times 9/10 = .947$

Let me know if you have questions.
Anonymous

3. I am not sure if that's correct.. I am understanding the problem this way:
If the polygraph is 92% reliable when given to someone who is guilty, and 95% reliable when given to someone who is innocent, this means that the probability of a suspect tested guilty given that he/she is actually guilty is 0.92 and the probability of a suspect tested innocent given that he/she is actually innocent is 0.95.

Let TG = tested guilty, TI = tested innocent

$P(TG|G)=0.92, P(TI|G)=0.08, P(TI|I)=0.95, P(TG|I)=0.05$

So $P(TG)=P(G)P(TG|G)+P(I)P(TG|I)=(0.1)(0.92)+(0.9)(0. 05)=0.137$
Right?

4. Originally Posted by dori1123
I am not sure if that's correct.. I am understanding the problem this way:
If the polygraph is 92% reliable when given to someone who is guilty, and 95% reliable when given to someone who is innocent, this means that the probability of a suspect tested guilty given that he/she is actually guilty is 0.92 and the probability of a suspect tested innocent given that he/she is actually innocent is 0.95.

Let TG = tested guilty, TI = tested innocent

$P(TG|G)=0.92, P(TI|G)=0.08, P(TI|I)=0.95, P(TG|I)=0.05$

So $P(TG)=P(G)P(TG|G)+P(I)P(TG|I)=(0.1)(0.92)+(0.9)(0. 05)=0.137$
Right?
Yes, you are correct. Anonymous1 was calculating the probability that the polygraph test was accurate, not the probability that the test says someone is guilty.