00:01
We know that a cancer test is 95 % accurate.
00:04
We also know the proportion of a population that has cancer.
00:08
Okay, so i'm going to turn this into probability notation so we can do some calculations.
00:13
The probability of having cancer, if you pick a random person, is 0 .005.
00:21
Now 95 % accuracy means that the probability of testing positive given you have cancer is 95%.
00:29
The probability of testing negative given you don't have cancer is 95%.
00:36
So it goes both ways.
00:38
We need both of those to be able to do this.
00:42
We want the probability of having cancer given the test is positive.
00:49
Okay, so when we want to flip conditional probability like this, we want to use bayes ' rule.
00:55
And i'll write out the formula we're going to use.
00:58
Probability of b given a is equal to a given b multiplied by b divided by a.
01:07
And this little bit here is equivalent to a and b.
01:14
A intersects b.
01:18
So what do we have? we need positive given cancer, we have that...