Two Plus Two Poker Forums How to account for probability in this case of chances of disease
 Register FAQ Search Today's Posts Mark Forums Read TwoPlusTwo.com

 Notices Expect about an hour of downtime for maintenance at around 6am ET on Wednesday.

 Probability Discussions of probability theory

 07-30-2020, 05:48 PM #1 Double Down veteran   Join Date: Oct 2003 Location: Studio City, CA Posts: 2,987 How to account for probability in this case of chances of disease Situation: A man has a son. The man is diagnosed in his early 40s with a deadly genetic disease, where there is a 50% chance that the child will also be a carrier of it (and die from it as well). Years later, the son is all grown up and is fifty years old. He is considering getting genetic testing to find out if he's a carrier. He does research on this disease and finds that for 80% of people who do have it, onset of symptoms happens between 30 and 50 years old. Is there a way to derive just from that what the odds are that he's a carrier? It seems intuitively that it's no longer 50/50, since the odds that he's not a carrier has to be higher than the odds that he is a carrier, but falls in the 20% category. How would you calculate the probability? Would it just be (50+20)/2= 35%? I guess I'm trying to figure out how to factor in "circumstantial" probability.
 07-30-2020, 06:11 PM #2 heehaww Pooh-Bah     Join Date: Aug 2011 Location: Tacooos!!!! Posts: 4,820 Re: How to account for probability in this case of chances of disease Apply Bayes' Theorem: P(have it) = .2*.5 / (.2*.5 + .5) = 1/6
07-31-2020, 12:08 AM   #3
Double Down
veteran

Join Date: Oct 2003
Location: Studio City, CA
Posts: 2,987
Re: How to account for probability in this case of chances of disease

Quote:
 Originally Posted by heehaww Apply Bayes' Theorem: P(have it) = .2*.5 / (.2*.5 + .5) = 1/6
I appreciate the response. I'm not that familiar with working with Bayes'Theorem but I think I get it, although I'm still not quite sure which pieces of info to fill into to which variables. What does the (.2*.5+.5) of the denominator represent?

Also, could you guys help me with one addition to this problem? (This is a personal thing happening, not for some exam or anything)

The 50 year old man dies suddenly soon after, so we never find out if he has the disease. He leaves behind two children. One of the children gets tested for the gene and is negative.

07-31-2020, 06:06 AM   #4
heehaww
Pooh-Bah

Join Date: Aug 2011
Location: Tacooos!!!!
Posts: 4,820
Re: How to account for probability in this case of chances of disease

Bayes Theorem: P(A given B) = P(A and B) / P(B) = P(A)*P(B given A) / P(B)

Applied here: P(have it | no symptoms before 50) = P(have it & no symptoms) / P(no symptoms)

Quote:
 The 50 year old man dies suddenly soon after, so we never find out if he has the disease. He leaves behind two children. One of the children gets tested for the gene and is negative. What can we now conclude about whether or not the dad had it?

P(had it) = P(had it & kid negative) / P(kid negative) = (1/6)(1/2) / (1/12 + 5/6) = 1/11

P(had it | no symptoms and kid negative) = .5*.2*.5 / (.5*.2*.5 + .5)

07-31-2020, 11:30 PM   #5
David Sklansky

Join Date: Aug 2002
Posts: 15,554
Re: How to account for probability in this case of chances of disease

Quote:
 Originally Posted by Double Down I appreciate the response. I'm not that familiar with working with Bayes'Theorem but I think I get it, although I'm still not quite sure which pieces of info to fill into to which variables. What does the (.2*.5+.5) of the denominator represent?
If you are willing to forget formulas, its simple logic. The probability that you are positive and get to 50 is 50% x 20% or 10%. The probability you are negative and get to 50 is (if you assume that nothing else could kill you) is 50% x 100% or 50%. 40% of the time you don't reach 50. Given you do (60%), 10 of that 60 you will be positive.

 08-01-2020, 12:31 AM #6 heehaww Pooh-Bah     Join Date: Aug 2011 Location: Tacooos!!!! Posts: 4,820 Re: How to account for probability in this case of chances of disease Basically the range of possibilities has been narrowed by the info. It's like, the chance of a spade is 1/4, but then if somehow you know that the card is black, that changes it to 1/2 because it's 13/26 instead of 13/52, or put another way, (1/4) / (1/2). Same thing here. Initially, the chance of being positive and asymptomatic is 50% * 20% = 10%. But then we're given the info that he's asymptomatic, so the possibility of being symptomatic is eliminated, like ruling out an answer to a multiple-choice test question. The eliminated possibility had a chance of 50% * 80% = 40%, so now our denominator shrinks from 100% to (100-40)%
08-03-2020, 08:24 AM   #7
nickthegeek
journeyman

Join Date: Sep 2011
Posts: 268
Re: How to account for probability in this case of chances of disease

Quote:
 Originally Posted by Double Down Is there a way to derive just from that what the odds are that he's a carrier?
In principle, you don't have enough information to answer. All the answers given had to make another assumption, which was not a given, and namely that the probability of having those symptoms is zero if you are not a carrier.

Suppose for instance that those symptoms are present even within the 80% of the healthy population. Having (or not having) them does not change the situation, and the man is still even money to be a carrier.

In another extreme situation, where 95% of the healthy people has those symptoms, actually not having them increases the chance that you are a carrier.

I illustrated the above examples just to let you understand what you need to properly answer and that you miss a bit of information: the probability of having (or not having) the symptoms if you are not a carrier.

I'd also add that making the assumptions that were made ITT could lead to totally irrational considerations were the question framed differently. I will point it out if there is any interest in it.

Last edited by nickthegeek; 08-03-2020 at 08:31 AM.

 08-03-2020, 10:19 AM #8 heehaww Pooh-Bah     Join Date: Aug 2011 Location: Tacooos!!!! Posts: 4,820 Re: How to account for probability in this case of chances of disease As usual, nickthegeek is right. In school I had a math teacher that used to say, "When you assume, you make an ass out of u and me."
 Yesterday, 03:52 AM #9 nickthegeek journeyman   Join Date: Sep 2011 Posts: 268 Re: How to account for probability in this case of chances of disease Thank you heehaww for your consideration (and btw I'm right much less often than "usually")! Pretty recently I was interested in this work, in which the authors postulate that the capability of taking rational decisions is a separate ability of the intelligence that doesn't get tested with standard IQ tests. The kind of "problems" that they propose to measure a "rationality quotient" is very similar to the one proposed here. It's pretty common for our brain to jump to some conclusions in some instances and being wrong. Just to outline how it's wrong to make assumptions (and how they mostly are unreasonable) let's consider these two variations. 1) You know that 80% of carriers support democracy. The man does not support democracy. 2) Same as the original question, but the man now does have symptoms. It's pretty clear in variation 1) that you don't have enough information to estimate the probability of the man being a carrier, and making assumptions would be pretty silly. Notice that the information you got is totally equivalent to the original question. More striking, in my opinion, is variation 2). Now, with the same assumption presented ITT, one should conclude that it's 100% sure, guarantee that the man is a carrier. I highly doubt that, if the question were presented as variation 2), anybody would assume that is 0 the probability of having symptoms if you are not a carrier. Last edited by nickthegeek; Yesterday at 03:58 AM.

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Forum Rules
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home Links to Popular Forums     News, Views, and Gossip     Beginners Questions     Marketplace & Staking     Casino & Cardroom Poker     Internet Poker     NL Strategy Forums     Poker Goals & Challenges     Las Vegas Lifestyle     Sporting Events     Other Other Topics Two Plus Two     About the Forums     Two Plus Two Magazine Forum     The Best of Two Plus Two Marketplace & Staking     Commercial Marketplace     General Marketplace     Staking - Offering Stakes     Staking         Staking - Offering Stakes         Staking - Seeking Stakes         Staking - Selling Shares - Online         Staking - Selling Shares - Live         Staking Rails         Transaction Feedback & Disputes     Transaction Feedback & Disputes Coaching & Training     Coaching Advice     Cash Game Poker Coach Listings     Tournament/SNG Poker Coach Listings Poker News & Discussion     News, Views, and Gossip     Poker Goals & Challenges     Poker Beats, Brags, and Variance     That's What She Said!     Legislation for Poker & Income Taxes for Poker Players     Twitch - Watch and Discuss Live Online Poker     Televised Poker General Poker Strategy     Beginners Questions     Books and Publications     Poker Tells/Behavior, hosted by: Zachary Elwood     Poker Theory     Psychology No Limit Hold'em Strategy     Medium-High Stakes PL/NL     Micro-Small Stakes PL/NL     Medium-High Stakes Full Ring     Micro-Small Stakes Full Ring     Heads Up NL     Live Low-stakes NL Limit Texas Hold'em Strategy     Mid-High Stakes Limit     Micro-Small Stakes Limit Tournament Poker Strategy     STT Strategy     Heads Up SNG and Spin and Gos     Mid-High Stakes MTT     Small Stakes MTT     MTT Community     Tournament Events Other Poker Strategy     High Stakes PL Omaha     Small Stakes PL Omaha     Omaha/8     Stud     Draw and Other Poker Live Poker     Casino & Cardroom Poker         Venues & Communities         Regional Communities     Venues & Communities     Tournament Events         WPT.com     Home Poker     Cash Strategy     Tournament Strategy Internet Poker     Internet Poker         Global Poker         BetOnline.ag Online Poker     Commercial Software     Software         Commercial Software         Free Software General Gambling     Backgammon Forum hosted by Bill Robertie.     Probability     Sports Betting     Other Gambling Games 2+2 Communities     Other Other Topics         OOTV         Game of Thrones     The Lounge: Discussion+Review     EDF     Las Vegas Lifestyle     BBV4Life         omg omg omg     House of Blogs Sports and Games     Sporting Events         Single-Team Season Threads         Fantasy Sports     Fantasy Sports         Sporting Events     Wrestling     Golf     Chess and Other Board Games     Video Games         League of Legends         Hearthstone     Puzzles and Other Games Other Topics     Politics and Society     History     Business, Finance, and Investing     Science, Math, and Philosophy     Religion, God, and Theology     Travel     Health and Fitness     Laughs or Links!     Computer Technical Help     Programming

All times are GMT -4. The time now is 12:13 PM.

 Contact Us - Two Plus Two Publishing LLC - Privacy Statement - Top