00:01
In this problem, we have been given some information about a certain test available to diagnose a disease.
00:07
Now, considering the information given in the question, let us define a few events.
00:12
Let d be the event that a person has the disease.
00:15
Then d complement will be the event that the person does not have the disease.
00:19
And let us consider n to be the event that the person tests negative.
00:24
Now, we have been asked to determine the probability that the person does not have the disease, given that the person tests negative.
00:31
So p of d complement given n.
00:33
Now to find this, we will use base theorem.
00:36
To use base theorem, we need a set of mutually exclusive and exhaustive events, so we will use d and d complement.
00:43
And using those two events and using base theorem, p of d complement given n will be equal to p of d complement times p of n given d complement, divided by p of d complement times p of n given d complement plus p of d times p of n given d.
01:03
So what is p of d complement? this will be 1 minus p of d using the complement rule of probability, and what is p of d? that is the probability of having the disease, and according to the question, that will be 0 .05.
01:17
Now, p of n given d complement is the probability of testing negative, given that the person does not have the disease...