Suppose that 5% of all students at Bruin State University have the freshman flu.

Question

Suppose that 5% of all students at Bruin State University have the freshman flu. This means that Pr(flu) -0.05 and Pr(no flu)- 0.95. There is an inexpensive test for the freshman flu, but it is unreliable. If a student has the freshman flu, the test will come back positive 90% of the time: Pr(positive|flu) = 0.90. However, the test will also come back positive 1% of the time when given to a student who doesn't have the flu: Pr(positivelno flu)0.01. 8 What is the probability that a randomly selected student will have a positive test result, i.e., what is Pr(positive)? Q9. Suppose that your roommate gets a positive test result. What is the probability that your roommate actually has the flu, i.e., what is Pr(flulpositive)?

Explanation / Answer

8. Pr(Positive) = P(Positive| Flu)*P(Flu) + P(Positive | No Flu)*P(No Flu) = 0.05*0.90 + 0.01*0.95 = 0.0545

9. P(Flu | Positive) = P(Positive and Flu) / P(Positive) = P(Positive | Flu)*P(Flu) / P(Positive) = (0.90*0.05)/0.0545

Hence,

P(Flu | Positive) = 0.8257 [Rounded off to 4 decimal places]

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