First day of class after the winter break and of course not much happened today, as we went through a few questions which are listed below. Other then that we discussed more about probability.
Suppose a test for cancer is 98% accurate. This means that the result of the test is correct 98% of the time. Suppose that 0.5% of the population has cancer. What is the probability that a person who tests positive has cancer? Suppose 1, 000, 000 randomly selected people are tested. There are 4 possibilities.
- A person with cancer tests positive
- A person with cancer tests negative
- A healthy person tests positive
- A healthy person tests negative
b) How many do not have cancer? 1, 000, 000 - 5000 = 995, 000
2) Assume the test is 98% accurate for people with cancer
a) How many people with cancer test positive? (5000)(.98) = 4900
b) How many people with cancer test negative? 5000 - 4900 = 100
3) Assume the test is 98% accurate for people without cancer
a) How many people without cancer test positive? 995, 000 - 975, 100 = 19, 900
b) How many people without cancer test negative? (995, 000)(.98) = 975, 100
4) a) How many people tested positive for cancer? 4900 + 19, 900 = 24, 800
b) How many of these people do have cancer? 4900
c) What is the probability that a person who tested positive for cancer actually does have cancer?
P(C|P) = 4900/(4900 + 19900)
P(P) = 0.0049 + 0.0199
P(C|P) = P(CP)/(P(CP) + P(HP))
P(H|N) = P(HN)/(P(CN) + (PHN))
= 0.9751/(0.975 + 0.0001)
I'm not too sure about what's going to happen tomorrow since I believe that a lot of people from class will be taking the English Provincial Exams so unless the scribe will be skipped to Wednesday the next person is Gerald.