Civilization Fanatics' Forums Test your knowledge of Probability

 Jun 26, 2011, 08:14 AM #1 ruff_hi Live 4ever! Or die trying     Join Date: Oct 2005 Location: an Aussie in NY Posts: 8,008 Images: 2 Test your knowledge of Probability Imagine that you are a physician and a 45-year-old patient of yours just had a positive mammogram. You also know the following facts:There is a 0.8 percent probability that a 40-to-50-year-old woman has breast cancer; If a woman has breast cancer, there is a 90 percent probability that she will have a positive mammogram; If a woman does not have breast cancer, there is a 7 percent probability that she will have a false positive mammogram. What do you tell your patient is the probability that she actually has breast cancer? __________________ My Blog [Getting Old, Getting Cranky], Wife's Series! [The Prism Series - book 2 The Deeper Darkness now on sale!] BUG Mod - BtS Unaltered Gameplay [ Forum | Download | FAQ | Known Issues | Report Bugs | Troubleshooting | BUG Wiki | Modding Tutorial | BUFFY ] "I found this great mod! Have you heard of it? It gives me everything I need!" - Troy Goodfellow's wife talking about the BUG mod Spawn Busting: All the cool guys are doing it | Ruff's Oz Game is now up and seeking your input! Test your knowledge of probability quiz! My latest game report - new 3/26
 Jun 26, 2011, 08:38 AM #3 JujuLautre Deity     Join Date: Apr 2007 Location: Kansai, Japan Posts: 3,090 I say 10% approximately __________________ Want to win on noble? Check my guide
 Jun 26, 2011, 08:46 AM #4 ori Repair Guy     Join Date: Dec 2005 Location: Baden-Württemberg, Germany Posts: 14,950 I agree with JujuLautre Spoiler for why it is 9.4%: 800 out of 100 000 women of that range would have BC, of these 720 would have a true positive mammogram 99200 out of 100 000 women would not have BC, of these 6944 would have a false positive mammogram -> the chance now for a true positive out of all positives is 720/(6944+720) *100 or 720/7664 *100 or 9.4% Moderator Action: please do make clear at some point soon, why this should stay in civ4 forums...
 Jun 26, 2011, 08:47 AM #5 AJ11 Emperor     Join Date: May 2011 Location: Sydney, Australia Posts: 1,013 7.664% Spoiler: Working it out: There is a 0.8% chance she will have cancer, or a 0.008 probability. There is a 99.2% chance that she will NOT have cancer, or a 0.992 probability. If she has, there is a 90% chance of returning a positive, or 0.9 probability. If she does not, there is a 7% chance of returning a positive, or a 0.07 probability. Thus, the chance of you saying "yes" will be: probability of cancer * probability of positive + probability of no cancer * probability of positive In numbers: (0.008 * 0.9) + (0.992 * 0.07) = 0.0072 + 0.06944 = 0.07664 or 7.664% EDIT: We had different interpretations of what he said :P Last edited by AJ11; Jun 26, 2011 at 08:53 AM.
 Jun 26, 2011, 09:31 AM #6 uat2d ಠ_ಠ     Join Date: Mar 2007 Location: Final Frontier Listening: House Posts: 2,707 Images: 4 I voted ~90%, but I was wrong when I did so. It's 63%. This is what we know: P(cancer) = .008 P(not cancer) = .992 P(positive mammogram|cancer) = .9 P(not cancer|positive mammogram) = .07 P(pm|c) = P(pm and c)/P(c) <=> P(pm and c) = 0.0072 P(nc and pm) = P(c)-P(c and pm) <=> P(nc and m) = 0.0008 P(nc|pm) = P(nc and pm)/P(pm) <=> P(pm) = 2/175 P(c|pm) = P(c and pm)/P(pm) <=> P(c|pm) = .63 Spoiler: P(x|y) means probability of x knowing that y c = cancer nc = not cancer pm = positive mammogram __________________ Piradinha! Ela tá maluca, ela tá doidinha!
 Jun 26, 2011, 09:37 AM #7 ori Repair Guy     Join Date: Dec 2005 Location: Baden-Württemberg, Germany Posts: 14,950 I could change your vote if you care about that...
Jun 26, 2011, 09:50 AM   #8
uat2d
ಠ_ಠ

Join Date: Mar 2007
Location: Final Frontier Listening: House
Posts: 2,707
Images: 4
Quote:
 Originally Posted by ori I could change your vote if you care about that...
If you don't mind, I'd appreciate it. Not that it matters much, but yeah, it would be kind of you.
__________________
Piradinha! Ela tá maluca, ela tá doidinha!

 Jun 26, 2011, 09:54 AM #9 babar Prince     Join Date: May 2010 Posts: 580 I must be terrible at probabilities, because I just can't see past 93%. (7% chance a positive result will be wrong, with the rest being irrelevant).
 Jun 26, 2011, 10:06 AM #10 ParadigmShifter Random Nonsense Generator     Join Date: Apr 2007 Location: Liverpool, home of Everton FC Posts: 21,816 It's just Bayes' Theorem http://en.wikipedia.org/wiki/Bayes'_theorem __________________ Most people think... Great God will come from the skies... Take away everything... And make everybody feel high (Bob Marley) Join the CFC Scrabble group! Discouraged in the gob
 Jun 26, 2011, 10:39 AM #11 mintegar Warlord     Join Date: Apr 2010 Posts: 236 my gut feeling is 0.8%, since just because of the positive test there is no way of knowing if it came from the (7% of 99.2%) of healthy women where the test comes back wrong, or from the (90% of 0.8%) of women with cancer.
Jun 26, 2011, 10:43 AM   #12
uat2d
ಠ_ಠ

Join Date: Mar 2007
Location: Final Frontier Listening: House
Posts: 2,707
Images: 4
Quote:
 Originally Posted by ParadigmShifter It's just Bayes' Theorem http://en.wikipedia.org/wiki/Bayes'_theorem

I never knew about that! It can make these kind of exercises so much more simple!

Not that I need it now for this exercise, but I'll add it to my calculator right away!
__________________
Piradinha! Ela tá maluca, ela tá doidinha!

 Jun 26, 2011, 10:58 AM #13 Kid R Emperor     Join Date: Jan 2009 Posts: 1,277 We have the results back from an apparently quite accurate test - it's not looking good for her at all.
 Jun 26, 2011, 11:24 AM #14 TheMulattoMaker Dictator of RF     Join Date: May 2008 Location: Far-GO! Posts: 1,017 I'd flip a coin, ignore the results, and go get a cup of coffee. Everybody be real happy that I work on electronics instead of people. __________________ . . Mr. BreadPants would like to wish everyone in CFC-land a Merry Pimpmas and a Happy End Turn. (Yes, PimpBob magically grows a third hand at Christmastime. I've learned not to question PimpBob.)
Jun 26, 2011, 12:53 PM   #15
ruff_hi
Live 4ever! Or die trying

Join Date: Oct 2005
Location: an Aussie in NY
Posts: 8,008
Images: 2
Quote:
 Originally Posted by ori Moderator Action: please do make clear at some point soon, why this should stay in civ4 forums...
because the understanding of probability and how it is sometimes misunderstood is fundamental to the combat engine underlying civ4. If people understood probability better, then their civ4 combat experience would be a happier event ...

Aggg - I just lost 3 95% victory battles in a row - that cannot happen!
__________________
My Blog [Getting Old, Getting Cranky], Wife's Series! [The Prism Series - book 2 The Deeper Darkness now on sale!]
BUG Mod - BtS Unaltered Gameplay [ Forum | Download | FAQ | Known Issues | Report Bugs | Troubleshooting | BUG Wiki | Modding Tutorial | BUFFY ]

"I found this great mod! Have you heard of it? It gives me everything I need!" - Troy Goodfellow's wife talking about the BUG mod
Spawn Busting: All the cool guys are doing it | Ruff's Oz Game is now up and seeking your input!

Test your knowledge of probability quiz! My latest game report - new 3/26

 Jun 26, 2011, 01:00 PM #16 ruff_hi Live 4ever! Or die trying     Join Date: Oct 2005 Location: an Aussie in NY Posts: 8,008 Images: 2 Now, on the flip side ... Imagine the above woman got a negative mammogram. Using the same information as above, what is the probability that she truly doesn't have breast cancer? __________________ My Blog [Getting Old, Getting Cranky], Wife's Series! [The Prism Series - book 2 The Deeper Darkness now on sale!] BUG Mod - BtS Unaltered Gameplay [ Forum | Download | FAQ | Known Issues | Report Bugs | Troubleshooting | BUG Wiki | Modding Tutorial | BUFFY ] "I found this great mod! Have you heard of it? It gives me everything I need!" - Troy Goodfellow's wife talking about the BUG mod Spawn Busting: All the cool guys are doing it | Ruff's Oz Game is now up and seeking your input! Test your knowledge of probability quiz! My latest game report - new 3/26
 Jun 26, 2011, 01:01 PM #17 r_rolo1 King of myself     Join Date: May 2006 Location: Lisbon, Portugal Posts: 13,818 @ post 15 Well, ruff, that is another issue OFC that people misunderstand odds a lot, but the example you are posting in the last post has some reasons ... linked to the fact that the RNG used in this game is quite more prone to rows of good/bad results than a actual random source ... the individual results are random enough, though ... __________________ " I'm the Lord of the lords, not the servant of the serfs" - D. João II of Portugal My Civ lema: Qui vincit non est victor nisi victus fatetur Lonely Hearts Club Bullpen / You , Yourself and your shadow : Some lessons on isolated starts
 Jun 26, 2011, 01:08 PM #18 martix Chieftain   Join Date: Mar 2010 Posts: 36 Also, PRNG's(like the one in the game) tend to exhibit anomalies on range boundaries. Meaning any comparisons with boundary conditions is gonna skew results even more.
Jun 26, 2011, 01:09 PM   #19
uat2d
ಠ_ಠ

Join Date: Mar 2007
Location: Final Frontier Listening: House
Posts: 2,707
Images: 4
Quote:
 Originally Posted by ruff_hi because the understanding of probability and how it is sometimes misunderstood is fundamental to the combat engine underlying civ4. If people understood probability better, then their civ4 combat experience would be a happier event ... Aggg - I just lost 3 95% victory battles in a row - that cannot happen!
Of course it can't happen, except on the 0.0125% of times it happens.

In fact, in only 14 battles with 95% odds, there's less than 50% chances you'll lose at least once. That cannot happen!
__________________
Piradinha! Ela tá maluca, ela tá doidinha!

Last edited by uat2d; Jun 26, 2011 at 01:16 PM.

Jun 26, 2011, 02:18 PM   #20
ori
Repair Guy

Join Date: Dec 2005
Posts: 14,950
Quote:
 Originally Posted by ruff_hi Now, on the flip side ... Imagine the above woman got a negative mammogram. Using the same information as above, what is the probability that she truly doesn't have breast cancer?

 Bookmarks

 Civilization Fanatics' Forums > Test your knowledge of Probability