A certain virus infects one in every 3000 people. A test...

A certain virus infects one in every 3000 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus, and 5% of the time if the person does not have the virus (false positive). Find the probability that a person has the virus given that they have tested positive. 0.0056 A person that tests positive, gets a second test that is also positive. Find the probability that the person has the virus. 0.00741

Transcript

00:01 So for this problem, we have that the probability of somebody being infected is equal to 1 in 500.

00:07 We're told that the probability of positive, given that the person has the virus, given that they're infected, is equal to 0 .9.

00:22 And the probability of positive given that somebody is not infected is equal to 0 .1.

00:30 So we can also say that the probability of negative, given infected, it's equal to 0 .1, and the probability of positive, or pardon me, probability of negative given not infected, is equal to 0 .9.

00:49 So, for part a, oh, let's see here, so i just need to slightly relabel my terminology for the events.

01:00 So we have a, that's the event that somebody is infected, and b is the event that somebody tests positive.

01:10 Anyways, so for part a, we're looking for the probability that somebody has the virus, so that's probability of event a, given that they tested positive.

01:20 So probability of a given b, which we can calculate as the probability of a and b, divided by the probability of b.

01:31 Which, in turn, the probability of a and b, we can calculate as the probability of b given a times the probability of a, then we divide that by the probability of b given a times probability of a, plus probability of b given not a times probability, oops, that's not a, times probability of not a.

02:01 So, looking at the values that we have, probability of b given a is 0 .9.

02:09 Probability of a is 1 over 500...

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