Question

A new simple fest has been developed to detect a particular type of cancer. The best must be evaluated before iti putin carcer. Each of the 2.000 adults is given the best and it is found that the best indicate cancer in 90% of those who have Amedical researcher les amandom sample of 2.000 adults and finds by the means at and in 2 of those who do not have is type of Based on these results, what is the probability of a randomly chosen person having and given that the best indicates cancer? found love decimal places ded) What is the probability of a person having cancer given that the best does not indicate cancer? (Round to decimal places as needed)

Answer 1

Here' the answer to the question. please write back in case you've doubts.

Filled the classification table according to the percentages mentioned in the question:

Test results/Actual-> | yes no - - - - - - - - - - - - - - - - - - - - - - - - - - - ---------------------------- yes 1.96*60 = 57.6. 1940*.02=38.8 no | 60-57.6 = 2.4| 1940-38.8=1902.2 2000 1.03*2000 = 60 | 2000-60 = 1940

Probability that a randomly chosen person having cancer given the test indicates cancer
= actually has cancer out of people who are tested +ive for cancer/total people tested +ive
= 57.6/(57.6+38.8)
= 0.598

Probability of a person having cancer given that the test does not indicate cancer:
= out of total -ive tested who actually had cancer /total -ive tested
= 2.4/(2.4+1902.2)
= 0.001260