This from 2009:
Yudkowsky poses the following canonical problem:
1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies.
A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?
The frightening thing is that only 15% of doctors get this right. And they’re off by a lot. That is, the average answer is in the range of 80% while the correct answer is 7.8%. Apparently, there is something about the way we think about the problem that makes 7.8% hard to accept, and Yudkowsky does a great job of walking you through the logic in painfully small steps.
Let’s try something similar here…
What Do We Know & What Does It Imply?
We have three pieces of information:
1% of sample are TRUE (that is, they have cancer)
80% of sample who are TRUE will test TRUE
9.6% of sample who are FALSE will test TRUE.
On the face of it, we should guess that the percentage of women who test TRUE who actually are TRUE (test positive and actually have cancer) is pretty small based on two facts provided: the actual percentage of women from the sample who are TRUE (regardless of testing) is only 1%, and the test has a false positive for 9.6% of those tested.
So, to solve this:
1) Assume we have a sample of 1000 women (I use 1000 to reduce the amount I have to talk about fractional people, but I don’t use 10,000 as I get lost in the zeros).
2) We know that the reality is that of the 1,000 women, 10 will have cancer (1%).
990 = no cancer
10 = cancer
3) Of the 10 who have cancer, 8 will test positive
8 out 1000 women tested will test True and are True
4) Of the 990 with no cancer 9.6% will also test positive = 990 * .096 = 95.04.
95.04 women out of 1,000 will test True but are False.
5) The total number testing true is 8 + 95.04 = 103.04.
Of these, 8 actually have Cancer.
6) So the value for tests positive (103.04) versus is positive (8) is 8/103.4 or 0.773 or 7.8%
I got good info from your blog
Normally I do not read post on blogs, but I wish to say that this write-up very forced me to try and do so! Your writing style has been surprised me. Thanks, quite nice article.
I believe you have mentioned some very interesting points, thankyou for the post.
I reckon something genuinely special in this web site.
This design is incredible! You most certainly know how to keep a reader entertained. Between your wit and your videos, I was almost moved to start my own blog (well, almost…HaHa!) Great job. I really loved what you had to say, and more than that, how you presented it. Too cool!
I together with my guys have already been going through the great key points found on your web site while all of a sudden got an awful suspicion I had not expressed respect to the web blog owner for those secrets. Most of the ladies ended up totally very interested to read through all of them and now have actually been using them. Thanks for simply being very accommodating as well as for picking out some notable information millions of individuals are really eager to understand about. Our honest apologies for not expressing appreciation to sooner.
I loved as much as you will receive carried out right here. The sketch is attractive, your authored subject matter stylish. nonetheless, you command get got an nervousness over that you wish be delivering the following. unwell unquestionably come further formerly again since exactly the same nearly a lot often inside case you shield this hike.
Hi , I do believe this is an excellent blog. I stumbled upon it on Yahoo , i will come back once again. Money and freedom is the best way to change, may you be rich and help other people.
Some genuinely great posts on this internet site, thanks for contribution. “Such evil deeds could religion prompt.” by Lucretius.
Just wanna comment on few general things, The website style is perfect, the written content is very wonderful. “The reason there are two senators for each state is so that one can be the designated driver.” by Jay Leno.
You made a number of good points there. I did a search on the subject matter and found the majority of people will have the same opinion with your blog.
The core of your writing while sounding agreeable at first, did not really sit perfectly with me personally after some time. Somewhere within the paragraphs you were able to make me a believer but only for a very short while. I still have a problem with your jumps in logic and you might do nicely to fill in all those breaks. When you can accomplish that, I would surely end up being impressed.
Respect to author, some great information .
certainly like your web site but you need to take a look at the spelling on several of your posts. Many of them are rife with spelling problems and I find it very bothersome to tell the reality then again I will certainly come again again.
A person essentially help to make critically posts I’d state. That is the very first time I frequented your website page and up to now? I amazed with the research you made to make this particular post amazing. Wonderful activity!
Hello would you mind letting me know which hosting company you’re using? I’ve loaded your blog in 3 completely different browsers and I must say this blog loads a lot quicker then most. Can you suggest a good hosting provider at a fair price? Thanks a lot, I appreciate it!
Write more, thats all I have to say. Literally, it seems as though you relied on the video to make your point. You definitely know what youre talking about, why waste your intelligence on just posting videos to your blog when you could be giving us something informative to read?
Wonderful blog! I found it while searching on Yahoo News. Do you have any suggestions on how to get listed in Yahoo News? I’ve been trying for a while but I never seem to get there! Many thanks
I’d have to examine with you here. Which is not one thing I usually do! I take pleasure in reading a post that may make folks think. Additionally, thanks for permitting me to comment!
Thank you for sharing with us, I think this website really stands out : D.
Some genuinely great posts on this web site, appreciate it for contribution. “For today and its blessings, I owe the world an attitude of gratitude.” by Clarence E. Hodges.
You really make it seem really easy along with your presentation however I find this matter to be really one thing which I think I might by no means understand. It sort of feels too complicated and extremely extensive for me. I’m having a look ahead on your next submit, I will try to get the hold of it!
Hiya, I’m really glad I’ve found this information. Today bloggers publish only about gossips and net and this is actually irritating. A good blog with exciting content, this is what I need. Thank you for keeping this website, I will be visiting it. Do you do newsletters? Can’t find it.
I keep listening to the news lecture about receiving free online grant applications so I have been looking around for the top site to get one. Could you tell me please, where could i find some?
I am often to blogging and i really appreciate your content. The article has really peaks my interest. I am going to bookmark your site and keep checking for new information.
Have you ever considered about including a little bit more than just your articles? I mean, what you say is fundamental and all. However just imagine if you added some great images or videos to give your posts more, “pop”! Your content is excellent but with pics and clips, this blog could definitely be one of the very best in its field. Wonderful blog!
Howdy very cool web site!! Man .. Excellent .. Wonderful .. I’ll bookmark your blog and take the feeds additionally?KI’m glad to search out numerous helpful info right here in the publish, we need work out extra techniques in this regard, thank you for sharing. . . . . .
Great paintings! That is the kind of info that are supposed to be shared across the internet. Disgrace on the seek engines for not positioning this post higher! Come on over and seek advice from my site . Thanks =)
I am glad to be one of many visitants on this great web site (:, appreciate it for putting up.
Valuable information. Lucky me I found your website by accident, and I am shocked why this accident did not happened earlier! I bookmarked it.
Terrific paintings! This is the type of info that are supposed to be shared around the net. Shame on the search engines for not positioning this publish higher! Come on over and talk over with my website . Thanks =)
Lovely just what I was searching for.Thanks to the author for taking his clock time on this one.
Hey there, You’ve done a great job. I’ll certainly digg it and for my part suggest to my friends. I’m sure they will be benefited from this site.
I’m impressed, I need to say. Actually not often do I encounter a blog that’s each educative and entertaining, and let me inform you, you may have hit the nail on the head. Your concept is excellent; the difficulty is one thing that not enough people are speaking intelligently about. I am very glad that I stumbled throughout this in my seek for one thing referring to this.
Wonderful blog you have here but I was wondering if you knew of any message boards that cover the same topics talked about in this article? I’d really love to be a part of community where I can get advice from other knowledgeable individuals that share the same interest. If you have any recommendations, please let me know. Kudos!
Hi, I think your site might be having browser compatibility issues. When I look at your blog site in Opera, it looks fine but when opening in Internet Explorer, it has some overlapping. I just wanted to give you a quick heads up! Other then that, very good blog!
LottoChamp is a specialized lottery prediction software designed to give players a statistical edge. Instead of relying on luck or random numbers, the platform uses mathematical algorithms and historical draw data to help users make more strategic number selections.
Well I really enjoyed studying it. This post offered by you is very helpful for proper planning.
I think this web site contains some real good info for everyone : D.
Fantastic beat ! I wish to apprentice whilst you amend your site, how can i subscribe for a blog website? The account helped me a acceptable deal. I were tiny bit acquainted of this your broadcast provided shiny transparent idea
PROSTADINE is truly unlike anything you’ve ever encountered in your life. It stands as the sole droplet solution that incorporates nine potent natural ingredients, working in perfect synergy to safeguard the health and mineral balance of your prostate well into your golden years.
Woah! I’m really loving the template/theme of this site. It’s simple, yet effective. A lot of times it’s challenging to get that “perfect balance” between superb usability and appearance. I must say that you’ve done a fantastic job with this. Additionally, the blog loads extremely fast for me on Firefox. Superb Blog!
Wonderful items from you, man. I have take into accout your stuff prior to and you are just extremely excellent. I actually like what you have got here, certainly like what you’re stating and the best way in which you say it. You’re making it entertaining and you continue to take care of to keep it smart. I can’t wait to learn far more from you. This is actually a tremendous website.
The ice water hack is a simple trick that involves using cold water to naturally activate your body’s thermogenic process. When you drink ice water, your body has to work harder to regulate its temperature, burning extra calories in the process.
I have been reading out a few of your stories and i can state pretty good stuff. I will definitely bookmark your blog.
Many men who have tried the blue salt trick report increased stamina, better performance, and a renewed sense of confidence.
There is noticeably a bundle to find out about this. I assume you made sure good factors in features also.
Some truly great content on this website , thanks for contribution.
Sleep Lean is a natural nighttime weight management supplement designed to help you burn fat, improve sleep quality, and balance hormones—all while you rest.
I?¦ll right away clutch your rss feed as I can not find your email subscription link or newsletter service. Do you’ve any? Kindly permit me recognise in order that I may subscribe. Thanks.