Question

Please help!!!

The test to detect the presence of a liver disorder is 98% accurate for a person who has the disease and 97% accurate for a person who does not have the disease.
If 3.5% of the people in a given population actually have the disorder, the probability that a randomly chosen person gets an incorrect diagnosis is

Answer 1

Do you know how to apply Bayes Theorem? Have you learned it yet?

Answer 2

One way to approach this is just by considering a group of people, say 10000 and then calculating each group. The key is to figure out which group you want the probability for.

Answer 3

@luffingsails No I haven't learned that. I got .02965 I don't know if it is right tho.

Answer 4

So, how did you approach your answer?

Answer 5

@luffingsails I multiplied .02 by .035 Because .02 of the .035 will have the disease. Then you factor in the 96.5 of the population do not have the disease, and .03 of those people have a false reading. so then you take this .035(.02) + .965(.03) and that is how I got my answer.

Answer 6

I think you are correct. I am going to use a tree approach (which is what you are applying before you use Bayes Theorem (which deals with calculating conditional probabilities).

(sorry I keep getting disconnected).

Answer 7

So, say our population is 10,000
The rate of people that have the disease is 3.5% (or 350 people out of our 10,000)

Answer 8

So, now we apply the other information.

If you have the disease (350) people, the test is 98% accurate. So 343 people will be accurately diagnosed and 7 people will get missed.

If you don't have the disease (9650), the test is 97% accurate. So, 9360.5 will be accurately diagnosed and 289.5 will be missed.

Answer 9

This is taking forever. I keep getting dumped!!! Sorry.

Answer 10

@luffingsails it's okay! So then do you add those together??

Answer 11

So, the total people missed is 289.5+7 = 296.5
P(of this group) = 296.5/10000 = 2.97%

Answer 12

Yes, exactly.

Answer 13

So, you were exactly correct in your answer. Just a long approach with more explanation from me. lol

Answer 14

@luffingsails Thank you!! I understand it so much better now.

Answer 15

Very good. Have a good day!