00:01
We have some information here.
00:02
I want to display it in probability notation.
00:06
So this blood test will give a positive result 90 % of the time.
00:10
So probability of testing positive given they have the disease is 90%.
00:16
Not point 9.
00:18
The probability of testing positive given they don't have the disease, so a complement to having the disease, no disease, is 25%.
00:28
The probability of having the disease, just in general, is 30%.
00:34
30 % of people have it.
00:37
So, what is the probability that if you test positive, you actually have the disease? so we want the probability of having the disease given tested positive.
00:49
So when you want to flip conditional probability, you want to use bay's rule.
00:55
And the formula is the probability of b given a is equal to a given b, multiplied by b, divided by a.
01:07
So we need positive given disease.
01:10
We have that.
01:11
We have the probability of having the disease.
01:14
We need to divide it by the probability of testing positive.
01:17
So we don't have that, but i can work it out.
01:20
There are two ways you might test positive.
01:23
You could test positive and have the disease.
01:29
This symbol is intersection, so positive and disease.
01:33
Or you could be positive and not have the disease.
01:36
And if i add these two probabilities up, i'll get the total probability of someone testing positive.
01:43
This numerator here, a given b, multiplied by b, is equal to a and b.
01:51
So positive and disease is 0 .9 times 0 .3.
01:57
That's 0 .27...