Finding the maximum percentage of people who are not in A or B [closed]

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
-1
down vote

favorite












60% of the population is in A
50% of the population is in B



To get the maximum number of people in neither, is it right to find the maximum number of people in both (50% in this case) and plug that in to the inclusion-exclusion formula?



(A or B) = A + B - (A and B) + None



So would the max of neither be 40%?




combinatorics inclusion-exclusion




share|cite|improve this question














closed as off-topic by amWhy, Xander Henderson, max_zorn, Shailesh, Leucippus Aug 19 at 5:20


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Xander Henderson, max_zorn, Shailesh, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.












  • Please read this MathJax tutorial, which explains how to typeset mathematics on this site.
    – N. F. Taussig
    Aug 18 at 6:58














up vote
-1
down vote

favorite












60% of the population is in A
50% of the population is in B



To get the maximum number of people in neither, is it right to find the maximum number of people in both (50% in this case) and plug that in to the inclusion-exclusion formula?



(A or B) = A + B - (A and B) + None



So would the max of neither be 40%?




combinatorics inclusion-exclusion




share|cite|improve this question














closed as off-topic by amWhy, Xander Henderson, max_zorn, Shailesh, Leucippus Aug 19 at 5:20


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Xander Henderson, max_zorn, Shailesh, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.












  • Please read this MathJax tutorial, which explains how to typeset mathematics on this site.
    – N. F. Taussig
    Aug 18 at 6:58












up vote
-1
down vote

favorite









up vote
-1
down vote

favorite











60% of the population is in A
50% of the population is in B



To get the maximum number of people in neither, is it right to find the maximum number of people in both (50% in this case) and plug that in to the inclusion-exclusion formula?



(A or B) = A + B - (A and B) + None



So would the max of neither be 40%?




combinatorics inclusion-exclusion




share|cite|improve this question














60% of the population is in A
50% of the population is in B



To get the maximum number of people in neither, is it right to find the maximum number of people in both (50% in this case) and plug that in to the inclusion-exclusion formula?



(A or B) = A + B - (A and B) + None



So would the max of neither be 40%?





combinatorics inclusion-exclusion





share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 18 at 6:56









N. F. Taussig

38.6k93053




38.6k93053










asked Aug 18 at 3:18









jl_

82




82




closed as off-topic by amWhy, Xander Henderson, max_zorn, Shailesh, Leucippus Aug 19 at 5:20


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Xander Henderson, max_zorn, Shailesh, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.




closed as off-topic by amWhy, Xander Henderson, max_zorn, Shailesh, Leucippus Aug 19 at 5:20


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Xander Henderson, max_zorn, Shailesh, Leucippus
If this question can be reworded to fit the rules in the help center, please edit the question.











  • Please read this MathJax tutorial, which explains how to typeset mathematics on this site.
    – N. F. Taussig
    Aug 18 at 6:58
















  • Please read this MathJax tutorial, which explains how to typeset mathematics on this site.
    – N. F. Taussig
    Aug 18 at 6:58















Please read this MathJax tutorial, which explains how to typeset mathematics on this site.
– N. F. Taussig
Aug 18 at 6:58




Please read this MathJax tutorial, which explains how to typeset mathematics on this site.
– N. F. Taussig
Aug 18 at 6:58










2 Answers
2






active

oldest

votes

















up vote
1
down vote



accepted










Another way to look at it:
$$beginalign|Acup B|+none&=100% Rightarrow \
none&=100%-|Acup B|=100%-(|A|+|B|-|Acap B|)=\
&=100%-60%-50%+|Acap B|=\
&=|Acap B|-10%.endalign$$
Hence, none (neither) is maximum $40%$ when $|Acap B|$ is maximum $50%$.






share|cite|improve this answer




















  • Thanks! Just realized I had my equations wrong, posted this late at night :/
    – jl_
    Aug 18 at 19:28

















up vote
1
down vote













Your equation is wrong, but your result is right. We have



$$
|Acup B|=|A|+|B|-|Acap B|
$$



(which corresponds to your equation without the “None” term), and since you want to minimize $|Acup B|$ with $|A|$ and $|B|$ given, you need to maximize $|Acap B|$.






share|cite|improve this answer



























    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    1
    down vote



    accepted










    Another way to look at it:
    $$beginalign|Acup B|+none&=100% Rightarrow \
    none&=100%-|Acup B|=100%-(|A|+|B|-|Acap B|)=\
    &=100%-60%-50%+|Acap B|=\
    &=|Acap B|-10%.endalign$$
    Hence, none (neither) is maximum $40%$ when $|Acap B|$ is maximum $50%$.






    share|cite|improve this answer




















    • Thanks! Just realized I had my equations wrong, posted this late at night :/
      – jl_
      Aug 18 at 19:28














    up vote
    1
    down vote



    accepted










    Another way to look at it:
    $$beginalign|Acup B|+none&=100% Rightarrow \
    none&=100%-|Acup B|=100%-(|A|+|B|-|Acap B|)=\
    &=100%-60%-50%+|Acap B|=\
    &=|Acap B|-10%.endalign$$
    Hence, none (neither) is maximum $40%$ when $|Acap B|$ is maximum $50%$.






    share|cite|improve this answer




















    • Thanks! Just realized I had my equations wrong, posted this late at night :/
      – jl_
      Aug 18 at 19:28












    up vote
    1
    down vote



    accepted







    up vote
    1
    down vote



    accepted






    Another way to look at it:
    $$beginalign|Acup B|+none&=100% Rightarrow \
    none&=100%-|Acup B|=100%-(|A|+|B|-|Acap B|)=\
    &=100%-60%-50%+|Acap B|=\
    &=|Acap B|-10%.endalign$$
    Hence, none (neither) is maximum $40%$ when $|Acap B|$ is maximum $50%$.






    share|cite|improve this answer












    Another way to look at it:
    $$beginalign|Acup B|+none&=100% Rightarrow \
    none&=100%-|Acup B|=100%-(|A|+|B|-|Acap B|)=\
    &=100%-60%-50%+|Acap B|=\
    &=|Acap B|-10%.endalign$$
    Hence, none (neither) is maximum $40%$ when $|Acap B|$ is maximum $50%$.







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered Aug 18 at 6:14









    farruhota

    14.1k2632




    14.1k2632











    • Thanks! Just realized I had my equations wrong, posted this late at night :/
      – jl_
      Aug 18 at 19:28
















    • Thanks! Just realized I had my equations wrong, posted this late at night :/
      – jl_
      Aug 18 at 19:28















    Thanks! Just realized I had my equations wrong, posted this late at night :/
    – jl_
    Aug 18 at 19:28




    Thanks! Just realized I had my equations wrong, posted this late at night :/
    – jl_
    Aug 18 at 19:28










    up vote
    1
    down vote













    Your equation is wrong, but your result is right. We have



    $$
    |Acup B|=|A|+|B|-|Acap B|
    $$



    (which corresponds to your equation without the “None” term), and since you want to minimize $|Acup B|$ with $|A|$ and $|B|$ given, you need to maximize $|Acap B|$.






    share|cite|improve this answer
























      up vote
      1
      down vote













      Your equation is wrong, but your result is right. We have



      $$
      |Acup B|=|A|+|B|-|Acap B|
      $$



      (which corresponds to your equation without the “None” term), and since you want to minimize $|Acup B|$ with $|A|$ and $|B|$ given, you need to maximize $|Acap B|$.






      share|cite|improve this answer






















        up vote
        1
        down vote










        up vote
        1
        down vote









        Your equation is wrong, but your result is right. We have



        $$
        |Acup B|=|A|+|B|-|Acap B|
        $$



        (which corresponds to your equation without the “None” term), and since you want to minimize $|Acup B|$ with $|A|$ and $|B|$ given, you need to maximize $|Acap B|$.






        share|cite|improve this answer












        Your equation is wrong, but your result is right. We have



        $$
        |Acup B|=|A|+|B|-|Acap B|
        $$



        (which corresponds to your equation without the “None” term), and since you want to minimize $|Acup B|$ with $|A|$ and $|B|$ given, you need to maximize $|Acap B|$.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Aug 18 at 5:53









        joriki

        165k10180331




        165k10180331












            -

            這個網誌中的熱門文章

            How to combine Bézier curves to a surface?

            圖片
            Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite My aim is to smooth the terrain in a video game. Therefore I contrived an algorithm that makes use of Bézier curves of different orders. But this algorithm is defined in a two dimensional space for now. To shift it into the third dimension I need to somehow combine the Bézier curves. Given two curves in each two dimensions, how can I combine them to build a surface? I thought about something like a curve of a curve. Or maybe I could multiply them somehow. How can I combine them to cause the wanted behavior? Is there a common approach? In the image you can see the input, on the left, and the output, on the right, of the algorithm that works in a two dimensional space. For the real application there is a three dimensional input. The algorithm relays only on the adjacent tiles. Given these it will define the control points of the mentioned Bézier cur...
            閱讀完整內容

            Mutual Information Always Non-negative

            圖片
            Clash Royale CLAN TAG #URR8PPP up vote 10 down vote favorite 6 What is the simplest proof that mutual information is always non-negative? i.e., $I(X;Y)ge0$ probability-theory share | cite | improve this question edited Jun 17 '12 at 15:38 Cameron Buie 83.6k 7 71 154 asked Jun 17 '12 at 15:30 Omri 359 3 13 3 Convexity of the function $tmapsto tlog t$. – Did Jun 17 '12 at 15:33 In addition, the convexity properties require the coefficients in the linear combination sum 1. Then, as p(x,y) is a probability distribution, it fullfits such condition. – Francisco Javier Delgado Ceped Aug 10 at 18:44 add a comment  |  up vote 10 down vote favorite 6 What is the simplest proof that mutual information is always non-negative? i.e., $I(X;Y)ge0$ probability-theory share | cite | improve this question edited Jun 17 ...
            閱讀完整內容

            Why am i infinitely getting the same tweet with the Twitter Search API?

            圖片
            up vote 0 down vote favorite My code workes perfectly for other queries, but for one query I am infinitely getting the same tweet. I can't understand what the problem is. API call: query='Allergic asthma OR Nonallergic asthma OR Occupational asthma OR EIB OR Exercise-induced bronchoconstriction OR Nocturnal asthma OR Cough-variant asthma' new_tweets = api.search(q=searchQuery, count=100, since_id=since_id, lang='en',tweet_mode='extended') if not new_tweets: print("No more tweets found") break for tweet in new_tweets: if True: print(jsonpickle.encode(tweet._json, unpicklable=False)) my_file = open('searchTweets.txt','a') my_file.write(jsonpickle.encode(tweet._json, unpicklable=False)+'n') my_file.close() else: continue Output in file: https://pastebin.com/JmRCsTeE These are the JSONs of the same Tweet. Other queries that work: Breast cancer OR Prostate cancer OR Colon cancer OR Lung cancer Type 2 dia...
            閱讀完整內容