The proportion of people in a given community who have a...

The proportion of people in a given community who have a certain disease is 0.005. A test is available to diagnose the disease. If a person has the disease, the probability that the test will produce a positive signal is 0.98. If a person does not have the disease the probability the test will produce a positive signal is 0.01. If a person tests positive, what is the probability they have the disease?

Transcript

00:01 In this question, we're given in a community.

00:04 Proportion of people having a certain disease is 0 .005.

00:08 A test is available to diagnose the disease.

00:12 Probability, the test will produce a positive signal is 0 .98 if the person has the disease.

00:19 And it will produce positive signal of 0 .01 if the person does not have the disease.

00:27 A person is tested positive.

00:30 I'm going to let d denote the event the person.

00:32 Person has the disease plus ve which is positive denote the event the person is tested positive minus ve denote the event the person is tested negative so i'm going to draw the probability tree event d and event d complement or d prime event d is the person having the disease d prime is the person does not have the disease so over here this is probability of event d that is the person having a disease, that is 0 .005.

01:12 Now we know that this part of the tree add up to total probability of 1.

01:16 So to get this part over here is probability of d prime, we take 1 minus 0 .005, and that will be 0 .995.

01:28 Now, each of this event is going to branch off to positive negative.

01:36 Positive is the person tested positive, and negative is the person tested negative.

01:44 Now over here this is probability of positive given d.

01:50 That is the person tested positive given he has the disease and there's 0 .98...