Question

6. The table below shows the soft drinks preferences of people in three age groups. If one of the 255 subjects is randomly selected, find the probability that the person drinks cola given the person is over 40 years of age. P(drinks cola| over 40 years of age) = ? Cola Root Beer Lemon-lime Under 21 years of age 40 25 20 Between 21 and 40 35 20 30 Over 40 years of age 20 30 35 7. Results from a Chembio test for hepatitis C among HIV-infected patients (based on data from a variety of sources) showed 337 subjects with positive test results including 2 false positive results. There were 1,163 negative results, including 10 false negative results. What is the probability that a randomly selected subject has a positive test result given he has no hepatitis C ?

Please show all work step by step and round answers to 4 decimals. thank you!

Answer 1

6. P(drink cola | over 40 years) = P(drink cola and over 40 year both) / P( over 40 years)

= (20/255)/( (20+30+35)/255) = 20 /85 = 0.2353

7). P(positive | no hepatitis) = ?

Now, as there are 337+1163 = 1500 patients

Now,

P( no hepatitis) = P(no hepatitis| negative results)* P(negative results) + P( no hepatitis | positive result (means false report) ) * P( positive results)

= 1153/1163* 1163/1500 + 2/337 * 337/1500

= 1155/1500. ( Because there are 10 false report in negative results and 2 false in positive result).

Now, P(no hepatitis and positive both) = P(no hepatitis | positive ) * P( positive)

= 2/337*337/1500 = 2/1500

Hence , P(positive| no hepatitis) = (2/1500)/(1155/1500) = 2/1155 = 0.0017