00:01
We're looking at a test for a coronavirus.
00:04
And let's convert the information we've been given into probability notation.
00:08
The probability that a randomly selected californian has coronavirus, so we'll put c, is 2 out of 1000.
00:17
So 0 .002, so it's 2 out of every 1000 habit.
00:22
There's a rapid test with a false positive rate of 2%.
00:27
So the probability of getting a positive result given you don't have covid, so c dash for c complement, is only 0 .02.
00:38
The false negative rate, so the probability of testing negative when you actually have it, is 0 .27.
00:45
So this is the information we have.
00:47
What is the probability you have it given it came back positive? so covid given positive.
00:56
When we want to flip conditional probability like this, we are going to be using bayes ' rule.
01:02
So i'll write this out.
01:07
The probability of b given a is equal to the probability of a given b multiplied by the probability of b divided by the probability of a.
01:19
So if we apply that here, we need positive given the coronavirus.
01:23
Well, we have negative given coronavirus, and everybody is either going to test positive or negative.
01:29
So if they don't test negative, they test positive.
01:32
So that would be 0 .73.
01:34
Probability of testing positive if you have it, we multiply that by the probability of having it and divide by the probability of testing positive in general...