5.X.X. Summary

Try these first

1. 1.

   What is a sample space?

   Hint

   Think about what all can happen in an experiment.

2. 2.

   What does conditional probability represent?

   Hint

   It involves two events and how they relate.

3. 3.

   What is the formula for Bayes’ Theorem?

   • A) P(A|B) = P(B|A) * P(A) / P(B)
   • B) P(B|A) = P(A|B) * P(B) / P(A)
   • C) P(B|A) = P(A) + P(B)
   • D) P(A|B) = P(A) + P(B)

   Hint

   Recall the components of the theorem.

4. 4.

   True or False: The posterior probability is the probability of an event after observing evidence.

   • True
   • False

   Hint

   Think about how evidence influences our prior beliefs.

5. 5.

   A certain type of rare cancer affects 0.1% of the population. A new test has a 95% sensitivity and a 10% false positive rate. Calculate the probability that a person has cancer given they tested positive.

   Hint

   Carefully analyze the components of Bayes' Theorem, paying attention to each probability involved.

6. 6.

   During an investigation, a witness claims to have seen a suspect at the crime scene. If there's only a 5% chance the witness is correct and this suspect has a prior probability of guilt of 20%, what is the updated probability of guilt if the evidence points to him?

   Hint

   Refer to previously covered definitions and remember to plug in values methodically into Bayes' Theorem.