The formula can be a quagmire if you don't relate it to relative frequencies, preferably with a tree.
I attached my assignment I'm working on....so I've tried it myself, not just looking for answers.
I think I got parts A and B correct....I think maybe I got c correct? But did it a weird way?
The Bonus question I'm totally lost.
Thanks for any help.
Thanks for the help! It sure does make it easier looking at it like that. Plus I see now that I got second numbers confused.
Just to make sure I'm getting the numbers right, for part b: TP/TP + FP = 8900 / (8900 + 2497500) = 0.004 rounded to 3 decimals or change my original b formula 0.750 number to 0.250.
for part c: T2P / (T2P + F2P) = 7921 / (7921 + 624375) = 0.013 rounded.
part d: TN/N 7492500/(7492500 + 1100) = 1.000 rounded. Did I do this one right here with your formula? Also, was my original correct? Was a total guess on this part....or did it just come out same answer but I did it wrong?
Thanks
You seem to be clear now on the reasoning with probabilities (though you'll need to translate into convential notation for conditional probabilities, as per the formula).
I'm just surprised you're willing to round so drastically. It may not look drastic, but rounding up to complete certainty and then plugging into further calculations is a no-no!
I can't tell if your use of the formula for d is correct (I agree that part a was fine apart from the switch) because I'm too confused by your values 'correct' vs. 'incorrect', which possibly could work but are a dangerous distraction in the tree that I've drawn.
Yeah I had an idea that I was supposed to extend the tree...just never did it before in class or in textbook more then original tree on 1 positive, which is why I was having some problems on this question, besides from the mix up on the numbers.
I agree using C is kind of a mess up....makes more sense to use Positive Test but I started with it so I guess just kept using it throughout.
Here is what looks like now.
Thanks for the help.....now I need to teach it to rest of class hah, since everyone I talked to was having issues with this. Happy I found this forum and your help.
Well, in b you switch back again to your original denominator. Which may not make any difference to your rounded answer but stop rounding!
c) is correct (but stop rounding!) and the method floats IF you read C as 'tests positive'.
d) is still up the creek. Your (unrounded) numbers in post 3 are all good. So why D (and not not D)? And please ditch the C and say P!
We were told to round all final numbers to 3 decimal places, which is why I was rounding like that at end.
Sorry but I'm not getting part d still
How would you set it up as a given that question with the bayes theorem? I tried fixing it...still got 1.000 which I think it right doing it the TN/N way. Also changed out C for P.
I'm getting confused when it says in question d, hint: re-adjust your probability tree.....to get those answers I just change around formulas and not tree....how does someone first testing negative supposed to change the entire tree?