Assignment:
An experimental test to detect a particular type of cancer indicates the presence of cancer in 90% of individuals known to have this type of cancer, and in 15% of individuals known to be cancer-free (false positive). One hundred individuals volunteer to take the test. Of the 100, 60 are known to have the cancer, and 40 are known to be cancer-free. If the test indicates that one of the individuals, randomly chosen, has the cancer, what is the probability that he or she is actually cancer-free?
Provide complete and step by step solution for the question and show calculations and use formulas.