Probability Rules
An Applied Example Walk-Through
Learning Objectives
Apply the probability rules to a real world problem
Conditional probabilities are used in so many contexts and so many places in the real world:
- What percent of people who view your ad click through?
- What percent of people will default on their mortgages if they rase interest rates?
- What percent of medical tests accurately report whether a person has an illness or not?
- What percent of people who have low incomes in the US survive cancer?
Example 16.1.1
Problem Setup: A patient takes a lab test and the result comes back positive.
- The test returns a positive result in 97% of the cases in which the disease is actually present.
- The test returns a negative result in 98% of the cases in which the disease is not present.
- 0.8% of all people have this illness.
Question:
- Can you write out the above sentences as probability expressions?
- Check your answers against the solutions below (click to reveal).
Solutions:
Example 16.1.2
Questions:
- What is the probability that the person tests positive and has the disease?
- What is the probability that the person tests negative and has the disease?
- What is the probability that the person tests positive and does not have the disease?
Instructions:
- Write out the probability expression for each above question.
- Check your answers against the solutions below (click to reveal).
Solutions:
Example 16.1.3
Instructions: Use the information from the previous section to solve for the probabilities:
- What is the probability that the person tests positive and has the disease?
- What is the probability that the person tests negative and has the disease?
- What is the probability that the person tests positive and does not have the disease?
Solutions: Click here to download the written solutions. Also see the next section for video solutions.
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