00:01
In this question, i've given probability a test for a disease correctly diagnosed a disease person as having the disease is 0 .95.
00:12
And probability the test incorrectly diagnosed someone without a disease as having the disease is 0 .1.
00:19
And 12 % of people in the population have this disease.
00:23
I'm going to let d denote the event a person has a disease.
00:28
Plus ve denote the event the person is tested positive.
00:34
And minus ve denote the event a person is tested negative.
00:38
So let's draw the probability three.
00:41
So event d, the person has a disease.
00:45
D prime or d complement, that is the person does not have the disease.
00:52
So the person having diseases 12 % probability.
00:56
That is 0 .12 in decimal.
00:59
We know this part of the probability three adds up to 1.
01:02
So probability of d prime will be 1 minus 0 .12 and that will be 0 .88.
01:14
So next is going to branch off to positive or negative, positive or tested negative.
01:25
Now this part here is probability of positive given event d.
01:33
That's the person has a disease and this will be 0 .95.
01:39
And over here, this is probability of positive given the complement.
01:47
That is the person is tested positive, but he actually does not have the disease.
01:54
And this would be 0 .1.
01:58
Now we want to find probability a person from this population will test positive for the disease.
02:03
So we're looking at probability of the event plus de.
02:08
Now, this would be two mutually exclusive events...