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?

Setting up an Applied Example

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: 

1. What is the probability that the person tests positive and has the disease?
2. What is the probability that the person tests negative and has the disease?
3. 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:

SOlving an Applied Example

Example 16.1.3

Instructions: Use the information from the previous section to solve for the probabilities:

1. What is the probability that the person tests positive and has the disease?
2. What is the probability that the person tests negative and has the disease?
3. 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.

Video Walkthrough of Applied Example

Your Own Notes (EXERCISE)

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