Bayes' rule

Lessons

• Introduction
  Deriving Bayes' rule

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• 1.
  Bayes' Rule
  I am going to ask my boss to be my reference after applying to another job. If she gives me a good recommendation there is a 0.75 probability that I will get the job. While if she gives me a bad recommendation there is only a 0.25 probability that I will get the job. There is a 60% chance she will give me a good reference and a 40% chance she will give me a bad reference.
  a)

  What is the probability that I will get the job?
  
  
  b)

  Given that I got the job what is the probability that she gave me a good reference
  
  

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• 2.
  I have 3 bags that each contains 5 marbles.
  

  Bag A:	Bag B:	Bag C:
  2 Green	4 Green	5 Green
  3 Red	1 Red	0 Red

  
  I roll a fair die to decide which bag I will draw from. If I roll a 1,2,3 I will draw a marble from Bag A. If I roll a 4,5 I will draw from Bag B. And if I roll a 6, then I will draw a marble from bag C.
  a)

  What is the probability that I draw a red marble?
  
  
  b)

  Suppose that I drew a green marble from a bag. What is the probability that I rolled a 6?
  
  

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• 3.
  False Positives
  A blood test is 95% effective when diagnosing a diseased person. However this blood test also incorrectly diagnoses a healthy person 5% of the time. If 0.1% of the population actually has this disease, then what is the probability that a person has the disease given that they tested positive?
  
  I like this, gives you hope if you get diagnosed for a serious disease
  Make note of how many healthy people and how many diseased people get diagnosed. Also make a tree diagram illustrating this.

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