Suppose that you are worried that you might have a rare disease. You decide to get tested, and suppose that the testing methods for this disease are correct 99 percent of the time (in other words, if you have the disease, it shows that you do with 99 percent probability, and if you don’t have the disease, it shows that you do not with 99 percent probability). Suppose this disease is actually quite rare, occurring randomly in the general population in only one of every 10,000 people.

If your test results come back positive, what are your chances that you actually have the disease?

Do you think it is approximately: (a) .99, (b) .90, (c) .10, or (d) .01?

Surprisingly, the answer is (d), less than 1 percent chance that you have the disease!

**Presentation Suggestions:**

After discussing the reasons for the surprising probability (below), you should see how changing the parameters affects the outcome. Would the result be so surprising if the disease were more common? How would the probability change if you allow the percentage of false positives and false negatives to be different?

**The Math Behind the Fact:**

This fact may be deduced using something called Bayes’ theorem, which helps us find the probability of event A given event B, written P(A|B), in terms of the probability of B given A, written P(B|A), and the probabilities of A and B:

P(A|B)=P(A)P(B|A) / P(B)

In this case, event A is the event you have this disease, and event B is the event that you test positive. Thus P(B|not A) is the probability of a “false positive”: that you test positive even though you don’t have the disease.

Here, P(B|A)=.99, P(A)=.0001, and P(B) may be derived by conditioning on whether event A does or does not occur:P(B)=P(B|A)P(A)+P(B|not A)P(not A)or .99*.0001+.01*.9999. Thus the ratio you get from Bayes’ Theorem is less than 1 percent.

The basic reason we get such a surprising result is because the disease is so rare that the number of false positives greatly outnumbers the people who truly have the disease. This can be seen by thinking about what we can expect in 1 million cases. In those million, about 100 will have the disease, and about 99 of those cases will be correctly diagnosed as having it. Otherwise about 999,900 of the million will not have the disease, but of those cases about 9999 of those will be false positives (test results that are positive because of errors). So, if you test positive, then the likelihood that you actually have the disease is about 99/(99+9999), which gives the same fraction as above, approximately .0098 or less than 1 percent!

Note that you can increase this probability by lowering the false positive rate.

Also note that these calculations wouldn’t hold if the disease were not independently and identically distributed throughout the population (e.g., in the case of cancer due to familial tendency, environmental factor, asbestos exposure, etc.).

safety insuranceGreat resources and tips for families here.

dua for husband to love his wife onlyDoes it look like we’re in for a big ride here?

JxcrTraureKakcompare/contrast essay example bullying essay header essay

JxecImileanalytical essay examples how to cite in essay how to cite a website mla in essay

Mdsmjdcasinos online term papers help i need a paper written for me

Wxevthoseto construct an effective ending to any type of essay, you should why uchicago essay examples how to write a good introduction for an essay

all blacks vs wallabies live onlineI’m impressed, I need to say. Really rarely do I encounter a blog that’s both educational and entertaining, and let me tell you, you have hit the nail on the head.

NxerImileto kill a mockingbird essay sample essay usc essay examples

metrolagu siteA thoughtful insight and ideas I will use on my blog. You’ve obviously spent some time on this. Congratulations

AqsEdistto construct an effective ending to any type of essay, you should 5 paragraph essay outline college essay word limit

mas informacionI like to spend my free time by scanning various internet resources. Today I came across your website and I found it has some of the most practical and helpful information I’ve seen.

germany dedicated serverWhen we look at these issues, we know that they are the key ones for our time.

Vclubshop loginYou ma’am have a way with words. Thank you very much!

JmgtTraureKakcialis 80mg benefits of cialis cialis reddit

mas informacionGreat resources and tips for families here.

informacion negocioYou ma’am have a way with words. Thank you very much!

empresaI saw a similar post on another website but the points were not as well articulated.

empresaIt’s clear you’re passionate about the issues.

negocioGood points – – it will make a difference with my parents.

Rpmqceazathioprine 25mg brand purchase digoxin micardis 20mg sale

shawarma in kubwaI wish I could craft such articles as this. Thank you very much.

vespa lx125 250 priceThere is so much to try to understand

informacionYou need to really control the comments listed here

EwbTaigocialis canadian cialis 20 mg price walmart cialis generika paypal

ventolin hfa asthma inhalerinhaler for asthma

thetechzoomOur family had similar issues, thanks.

노팔로우I like to spend my free time by scaning various internet recourses. Today I came across your site and I found it is as one of the best free resources available! Well done! Keep on this quality!

macular degeneration cure treatmentHowdy, a helpful article for sure. Thank you.

zaragozahave already been reading ur blog for a couple of days. really enjoy what you posted. btw i will be doing a report about this topic. do you happen to know any great websites or forums that I can find out more? thanks a lot.

best remote desktop softwareLike the way you’ve outlined things. Easy to follow. Not cluttered.

노팔로우줘요That’s some inspirational stuff. Never knew that opinions might be this varied. Thanks for all the enthusiasm to supply such helpful information here.

Qu'est ce qu'on a tous fait au Bon Dieu 3 StreamingOur local network of agencies has found your research so helpful.

Amsterdam 2022 PutlockerWhen we look at these issues, we know that they are the key ones for our time.

facebook instant articleWhen are you going to take this to a full book?

Ndoqbgbuy motrin 600mg pill remeron 30mg oral order rocaltrol online

llaves coches en madridThe clarity in your post is just nice and I can tell you are an expert in the subject matter.

ventanas madridGreat info! Keep post great articles.

azithromycin pills 250 mghttps://zpack.beauty z pack antibiotic

ล้นเป๋าI’ve thought about posting something about this before. Good job! Can I use part of your post in my blog?

ventanas aluminioDeveloping a framework is important.

JniImileis bactrim sulfa based bactrim dosage bactrim balsamico precio

federal hammerdown 357I have been curious about these trends, and you have really helped me. I have just told a few of my friends about this on FaceBook and they love your content just as much as I do.