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anonymous
 one year ago
I need someone to explain this to me, I really don't understand...
Using Baye's Theorem:
It is known that 2% of the population has a certain allergy. A test correctly identifies people who have the allergy 98% of the time. The test correctly identifies people who do not have the allergy 94% of the time. A doctor decides that anyone who tests positive for the allergy should begin taking antiallergy medication. Do you think this is a good decision? Why or why not?
I know it's pretty long and a little bit of reading but it's on paper so I had to copy it, I wouldn't have if I didn't need the
anonymous
 one year ago
I need someone to explain this to me, I really don't understand... Using Baye's Theorem: It is known that 2% of the population has a certain allergy. A test correctly identifies people who have the allergy 98% of the time. The test correctly identifies people who do not have the allergy 94% of the time. A doctor decides that anyone who tests positive for the allergy should begin taking antiallergy medication. Do you think this is a good decision? Why or why not? I know it's pretty long and a little bit of reading but it's on paper so I had to copy it, I wouldn't have if I didn't need the

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0this is often very confusing one good way to approach this is to use some actual numbers and see what happens

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it makes "baye's theorem" far more undersantable

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay but how do I choose my numbers?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i would pick a large number for the population, so that we get all whole number answers (although once we get the answer, we can redo it without using that crutch) lets say the population is 1000 people ok?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and if 2% of the population suffers from the allergies, how many people exactly will have it? i.e what is 2% of 1000 ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Umm...40? I'm not sure I did this right

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oops sorry that is wrong

anonymous
 one year ago
Best ResponseYou've already chosen the best response.02% of 1,000 is \(.02\times 1000=20\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that is why i picked a nice round number like 1000 so the it would be easy to compute the percents

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That what I did but my calculator said i was 40...oh well what do I have to do next?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so 20 people have the allergy, how many do not?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0By the way that already helps a lot

anonymous
 one year ago
Best ResponseYou've already chosen the best response.020 out of 1000 which is... 20/10000=0.2%?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hold on i think i have confused you

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0we have a population of 1,000 2% have the allergy, so 20 have the allergy if out of 1,000 people, 20 have the allergy, how many (not what percent) do not have the allergy

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ooooh, sorry with the 10000 I got confused with another problem on my paper sorry. Umm so 980 don't have the allergy?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so we know how many have it, and how many do not now lets see how many people will test positive for it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0of the 20 people that have it, the test is 98% accurate what is 98% of 20?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0btw i hope it is clear that you do \(.98\times 20\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah I'm good with the percentage....most of the time

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i guess we have to work with the decimal, should have chosen a population of 10,000 then it would be whole numbers but too late now

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now we know \(980\) so NOT have the allergy, lets see how many of those will also test positive

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0for them the test is 96% accurate so 96% of them will test negative, but that means 6% of them will test positive what is 6% of 980?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.04% will test positive what is 4% of 980

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so now how many people total (it is a decimal) will test positive?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.00.04 people? I'm confused

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0we computed two numbers of people that test positive right? the ones with the allergy, 19.6 and the ones without the allergy, 39.2 what is the total?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0right, that is the total number that test positive

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0out of those, we know that 19.6 actually have the allergy

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the question is, IF you test positive, what is the probabilty you actually have the allergy that is the number of people who test positive and have the allergy, divided by the total number of people who test postive ie\[\frac{ 19.6}{58.8}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0or whatever you get when you write that as a decimal, i get \(0.337\) rounded, a little more than a third

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay I get 0.33333etc.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh maybe i put the wrong numbers in yeah you are right

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0one third in other words

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would you like to redo this using "baye's formula" ? will will do pretty much the same arithmetic, and get the same answer

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah, it would help a lot, my teacher just throws a formula and exercises at us

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok do you have the formula you are supposed to use? i can make a guess if you like

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0go ahead and write it, we can walk through it slowly

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It's \[P(AB)=\frac{P(AB)*P(A)}{ P(B)}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I have it right in front of me

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0first off, it this is going to make sense, you need to know what \(P(AB)\) means do you know what it means?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh crap your definition is wrong, but we will get to that in a second

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It means probability of A given B

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and the definition (not baye's theorem) is \[P(AB)=\frac{P(A\cap B)}{P(B)}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0My teacher made us study about a formula like that, but I really didn't get a thing

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0baye's theorem, at least one form, is not quite what you wrote, the condition is switched on the right it is \[P(AB)=\frac{P(BA)*P(A)}{ P(B)}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok lets see if we can get it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok now the numerator in your fraction \[P(BA)P(A)\] is just another way to find \(P(A\cap B)\) the probability that both A and B occur

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That's where I get extremely confused

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0lets use our example you want the probability you have the allergy GIVEN you test positive

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0we can put A = you have the allergy, B = you test positive then we are trying to find \(P(AB)\) the probability you have the allergy given that you test positive

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0let me know if i lost you, we need to go slow i am sure

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay so far I think I'm okay...I think so for now

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok to compute that we need the numerator \(P(A\cap B) \) i.e. the probability you have it AND test positive we were not told that number

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but we were told \(P(B)\) the probabily you have the disease, that was \(2\%=0.02\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and we were also told \(P(BA)\) the probability you have the disease given that you test positive that was the \(98\%=0.98\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0to find the numerator, multiply those together, i.e. the probability you have the disease AND test positive is the probability you have the disease times the probability you test positive GIVEN that you have the disease, i.e. \[.02\times.98=.0196\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you notice that is the same numerator we had before, just with the decimal moved over three places, because we did not start out with a population of 1,000 we just went straight for the number

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wait why did you change the 98% to a decimal. to make it easier to work with?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0when doing any work in math, you use numbers, not percents \(98\%=0.98\) as a number percents are nice to look at, but think about what you did when you wanted to find 98% of 20 you multiplied 20 by .98 right, not by 98

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ready to find the denominator?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that is \(P(B)\) the probability you test positive remember how we found that before? we had to add two numbers, they were \(19.6\) and \(39.2\) they will be the same this time, but with the decimal in a different place

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the fist one is the \(.00196\) we already found, that is the number of people who test positive given that they have the disease

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so you divided it by 1000 right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0we also need the number of people who test positive who do NOT have the disease

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well, yes, but we just found again computing \(.02\times .98=.00196\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0to compute the probability that you test positive if you do not have the disease we used \(.04\times .980=.0392\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm sorry I really want to learn but I have to go to bed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now add together to get the probability you test positive, that is \(.00196+.00392=.00588\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you did help a lot already though I'll make sure I have a lot of time next time I ask a question though

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah it is late you can look at this later and see that we are really using the same numbers as before
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