Worksheet 7: Bayes’ Rule

Worksheet 7: Bayes’ Rule#

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  1. How confident should the doctor be that the patient has the disease, given that the test came back positive?

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Let \(A\) be the event that the patient has the disease, and let \(B\) be the event that the test is positive.

  1. How can we express the accuracy of the test in the language of conditional probabilities? \vspace{2.5cm}

  2. How can we express our confidence that the patient has the disease, given that the test is positive, in the language of conditional probabilities? \vspace{2.5cm}

  3. How would you express \(\Pr[\overline{A} \mid B]\) in plain English? \vspace{2.5cm}

Bayes’ Rule is the following rule for computing conditional probabilities:

\[ \Pr[A \mid B] = \Pr[B \mid A] \cdot \frac{\Pr[A]}{\Pr[B]}. \]

  1. Use Bayes’ Rule to compute \(\Pr[A \mid B]\).