A certain test for mononucleosis has a 99% chance of correctly diagnosing a patient with mononucleosis and a 5% chance of misdiagnosing a patient who does not have the infection. Suppose the test is given to a group where 1% of the people have mononucleosis. If a randomly selected patient's test result is positive, what is the probability that she has mononucleosis? Explain.
An exercise, commentary, and solution from Illustrative Mathematics
Students use the complement rule to calculate the probability of the complement of an event and the multiplication rule for independent events to calculate the probability of the intersection of two independent events. Students recognize that two event A and B are independent if and only if P(A and B) = P(A)P(B) and interpret independence of two events A and B as meaning that the conditional probability of A given B is equal to P(A). Students use the formula for conditional probability to calculate conditional probabilities and interpret probabilities in context.
Teacher and Student versions of full lesson from engageNY
Additive and Multiplicative Rules for Probability In this Concept, you will learn how to combine probabilities with the Additive Rule and the Multiplicative Rule. Through the examples in this lesson, it will become clear when to use which rule. You will also be presented with information about mutually exclusive events and independent events.
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