Topic 6: Understanding Chance Flashcards
What is prosecutor’s fallacy?
The prosecutor’s fallacy is a misconception that arises when the probability of a particular event occurring is incorrectly interpreted based on conditional probabilities.
It is a mistake where it is assumed that probability of a random match (on DNA or fingerprints) is equal to probability that the defendant is innocent
What is an example of prosecutors fallacy and its flaws
Suppose 5 million people live in Sydney. A murder occurs with DNA left on the weapon. A person matching the DNA is arressted.
Faulty argument:
Chance of a positive dna match is 1 in 500000, hence chance that arrest person is guilty is very high
Hence, the chance that DNA matches given innocence is tiny, but the chance that the person is innocent given DNA match = 0.9 = high. So for any person with DNA match, we can’t say p (guilty | DNA match) is high
We cant be thinking about the probability that a person has a positive DNA match given they are innocent, but focus on probability they are innocent given a DNA match –> more accurate measure of someones innocence
What are 4 basic properties of cahnce?
Chances are between 0 (impossible) and 1 (certain) (or 0% to 100%)
Chance of something = 100% - its complement
Drawing at random means collection of objects have same chance of being picked
What is conditional probability/
Probability that a certain event occurs given another event has occurred
What is the equation of conditional probability
P(A | B) = P (A ∩ B) / P (B)
What is the multiplication principle
States that probability that 2 events occur is chance of 1st event x chance of 2nd event, given the 1st has occurred
P (A and B occur) = P(A) x P(B | A)
What is independence?
2 events are independent if the chance of the 2nd given the 1st is the same as the 2nd.
Drawing randomly with replacement ensures independence
What is dependence
2 events are dependent if the chance of the 2nd given the 1st is dependent on the result of the 1st
I.e. drawing without replacement
How do we solve simple chance problems?
1) Write a list of all outcomes
2) Count which outcomes belong to an event of interest
We can do all of this through:
Writing a full list of outcomes and count outcomes of interest OR summarise in a tree diagram and count outcomes of interest OR use R to simulate repetition
What does mutually exclusive mean
Is when occurrence of one event prevents the other
What rule do we use when two events are mutually exclusive
we use addition rule
Binomial model and binomial theory and coefficient, check in books
Check books
