Bayes Theorem Question - Am I doing this right?

In summary, the lie detector is 95% reliable when the person is guilty and 98% reliable when innocent. When a random person is pulled from a pool of people with 6% guilty of theft and 94% innocent, the probability of them being guilty based on a positive lie detector test is 75.20%. This is a famous paradox where a test with high accuracy can still be unreliable when the population is mostly negative.
  • #1
RedPhoenix
26
0
Another Conditional Problem...

Lie Detector is
95% reliable when the person is guilty
98% reliable when innocent

Random Person pulled from a pool of people... This pool is 6% guilty of theft and 94% have never stolen...

Random person was determined guilty from the lie detector, what is the probability he is innocent?

-------------------------------
My attempt...

(.95)(.06) / [(.95)(.06) + (.02)(1-.06)] = .7512 . so 75.12% chance of him being guilty. Seems low, but I guess the fact that the pool of people has only 6% guilty in it, it lowers the chance a lot.
 
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  • #2
I get
(.95)(.06) / [(.95)(.06) + (.02)(1-.06)] = .7520
This is a famous paradox
If a test is fairly accurate, but the population mostly negative a positive test is not very reliable.
 
  • #3
lurflurf said:
I get
(.95)(.06) / [(.95)(.06) + (.02)(1-.06)] = .7520
This is a famous paradox
If a test is fairly accurate, but the population mostly negative a positive test is not very reliable.

Pretty crazy, but thanks for the help :)
 

1. What is Bayes Theorem?

Bayes Theorem is a mathematical formula that calculates the probability of an event occurring based on prior knowledge and evidence.

2. How do I use Bayes Theorem?

To use Bayes Theorem, you need to have prior knowledge or information about the likelihood of an event occurring. You also need to have new evidence or observations that can help update this prior knowledge. The theorem uses this information to calculate the probability of the event occurring.

3. What is the formula for Bayes Theorem?

The formula for Bayes Theorem is P(A|B) = (P(B|A) * P(A)) / P(B), where P(A|B) is the probability of event A occurring given event B has occurred, P(B|A) is the probability of event B occurring given event A has occurred, and P(A) and P(B) are the probabilities of events A and B occurring independently.

4. How do I know if I am using Bayes Theorem correctly?

To ensure you are using Bayes Theorem correctly, you need to make sure that you are using the correct formula and plugging in the correct values for the prior knowledge and evidence. You should also check that the probabilities you are using are accurate and updated.

5. What are some common applications of Bayes Theorem?

Bayes Theorem is commonly used in fields such as statistics, machine learning, and artificial intelligence. It is used to make predictions, update beliefs, and analyze data in various industries such as finance, healthcare, and marketing.

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