Probabilities magine there is a town with 10,000 people. All of them get a test

Question

Probabilities magine there is a town with 10,000 people. All of them get a test for disease X_The 1% of the people actually have disease X. The false positive rate for the disease is 5%. 3A. How many people in the town have the disease? 3B. How many don't have the disease? 3C. How many people who don't have the disease still get a positive test result? 3D. How many people in total got a positive test result? 3E. Maria lives in this town and got a positive test result. What is the probability that she actually has the disease? 3F Bonus.question, Mark also lives in the same town, but he is the only person in the town who didn't get a test done. What do you think is the probability that he has the disease? | I Print Layout View Sec 1 81% emmmmmt

Explanation / Answer

Number of people tested positive = Percentage of people producind disease * Population size /100 = 1*10000/100=100

False positive percentage = 5%

Number of people with false poisitive result = False positive percentage*Number of people with positive result/100 =5*100/100=5

Actual number of people with disease = Number of people with positive result-Number of people with false poisitive result =100-5=95

3A. Number of people having the disease = 95

3B. Number of people not having disease = 10000-95 = 9905

3C. Number of people not having disease, but testing positive = 5

3D. Number of people tested positive = 100

3E. Probabiltiy of Maria having disease = 100-False positive percentage = 100-5=95%

3F. Probabiltiy of Mark having disease = (100-False positive percentage)/(100*Percentage of people having disease) =(100-5)/(100*1)=0.95%

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