A certain screening process is used to detect the potential...

A certain screening process is used to detect the potential presence of cancer. For people with this form of cancer, there are approximately 16% false negatives among all screenings. That is, given a person has this form of cancer, the probability they will test negative is 0.16. For people without the cancer, there are approximately 19% false positives among all screenings. In the United States, about 8 in 100,000 people have this cancer.

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00:01 So we're looking at a test for cervical cancer, and we have some probabilities.

00:06 I'm going to write them out in probability notation.

00:10 So for women with this cancer, there are 16 % false negatives.

00:15 So probability of testing negative, given they have cancer, is 16%.

00:22 The probability of testing positive, given someone doesn't have cancer, so a false positive, is 19%.

00:29 The probability of having cancer is 8 out of 100 ,000.

00:36 0, 0, 0, 0, 0, 0, 0, 0.

00:43 Okay.

00:46 So we want to find out the probability where if somebody tests positive, they have cancer.

00:53 So we want the probability of cancer given positive.

00:58 When you want to flip conditional probability like this, you're going to be using bay's rule, which is the probability of b given a is equal to probability of a given b, multiplied by b, divided by a.

01:18 So here we need positive given cancer.

01:22 Well, i have negative given cancer, and everybody tests either positive or negative.

01:27 So positive would be 0 .84, multiplied by the probability of having cancer, which i'll just put 8 over 100 ,000, divided by the probability of testing positive.

01:41 So i don't have that, but i can calculate it.

01:46 So everybody who tests positive either has cancer or they don't...

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