I have the following task: There is 4% of sick people in a population. There is 5% chance for a positive test for a healthy person. There is 2% chance for a negative test for a a sick person. We tested 100 people and 4 had a positive test. What is the probability of such an outcome?
So far I found that the probability for a test to be positive is 0.086, but I am not sure what to do next.
On
Take this answer with a grain of salt, and call me in the morning. The probability of getting a positive result is .0872, as they commented above. IF the probability follows the binomial PMF, then (nCk)(p^k)(q^n-k) gives .0356 or 3.5%. If there is a different distribution, then we may be off the mark.
Assuming your overall positivity rate is correct: You then have a binomial probability situation where you want to know the probability of 4 successes in 100 trials.