A false positive rate of 5% is considered to be a conservative estimate. Suppose that there are 20 employees in your company, which tests its workers weekly. What is the probability of no false-positives for this week’s test?
To calculate the probability of no false positives for this week's test, we need to use the false positive rate and the number of employees in the company.
Given that the false positive rate is 5%, this means that for any given employee, there is a 5% chance of a false positive result.
Since there are 20 employees in the company, we can treat each employee's test result as an independent event. Therefore, we can calculate the probability of no false positives for this week's test as the probability that all 20 employees have negative test results.
To calculate this probability, we need to multiply the probability of each employee having a negative test result.
The probability of one employee having a negative test result is 1 - the false positive rate. In this case, it is 1 - 0.05, which is 0.95.
Since there are 20 employees, we multiply this probability 20 times:
Probability of no false positives = (0.95)^20
Using a calculator or software, we can calculate this probability:
Probability of no false positives ≈ 0.3584859224
Therefore, the probability of no false positives for this week's test is approximately 0.358 or 35.8%.