Probability of that n children are daughters given at least one daughter, using set theory

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











up vote
-3
down vote

favorite












Here is a question that I would like to dolve using set theory. I know the answer but was not able to solve it with Set Theory. The question goes as follows: a father has n children, given that the father has at least 1 daughter, what is the probability of n daughters?
Here's my attempty using Set Theory:
Let G be the event of all girls defined to be g1^g2^...^gn and let B be the event of all boys defined to be b1^b2^...^bn. Let !B be defined as the complement of all boys which is also the event of at least one girl. So here !B = !(b1^b2^...^b3) which is then !B = !b1/!b2/.../!bn. Then I tried applying Bayes Rule such that P(G|!B) = P(G^!B)/P(!B). So here is where I run into a problem, P(G^!B) = P(G^(!b1/!b2/.../!bn)) = P((G^!b1)/(G^!b2)/.../(G^!bn)) = P(!b1/!b2/.../!bn). This makes sense to me as the set of all girls intersected by the set of at least one girl should be equivalent to the set of at least 1 girl. However this would mean that P(G|!B) = P(!B)/P(!B) = 1. Obviously this is wrong but I don't understand where. Your advice is very much appreciated







share|cite|improve this question


















  • 1




    This does not seem to have much to do with set theory ...
    – Henning Makholm
    Aug 20 at 9:34










  • The question presumes binary genders. Please formulate it in an inclusive manner.
    – joriki
    Aug 20 at 9:45














up vote
-3
down vote

favorite












Here is a question that I would like to dolve using set theory. I know the answer but was not able to solve it with Set Theory. The question goes as follows: a father has n children, given that the father has at least 1 daughter, what is the probability of n daughters?
Here's my attempty using Set Theory:
Let G be the event of all girls defined to be g1^g2^...^gn and let B be the event of all boys defined to be b1^b2^...^bn. Let !B be defined as the complement of all boys which is also the event of at least one girl. So here !B = !(b1^b2^...^b3) which is then !B = !b1/!b2/.../!bn. Then I tried applying Bayes Rule such that P(G|!B) = P(G^!B)/P(!B). So here is where I run into a problem, P(G^!B) = P(G^(!b1/!b2/.../!bn)) = P((G^!b1)/(G^!b2)/.../(G^!bn)) = P(!b1/!b2/.../!bn). This makes sense to me as the set of all girls intersected by the set of at least one girl should be equivalent to the set of at least 1 girl. However this would mean that P(G|!B) = P(!B)/P(!B) = 1. Obviously this is wrong but I don't understand where. Your advice is very much appreciated







share|cite|improve this question


















  • 1




    This does not seem to have much to do with set theory ...
    – Henning Makholm
    Aug 20 at 9:34










  • The question presumes binary genders. Please formulate it in an inclusive manner.
    – joriki
    Aug 20 at 9:45












up vote
-3
down vote

favorite









up vote
-3
down vote

favorite











Here is a question that I would like to dolve using set theory. I know the answer but was not able to solve it with Set Theory. The question goes as follows: a father has n children, given that the father has at least 1 daughter, what is the probability of n daughters?
Here's my attempty using Set Theory:
Let G be the event of all girls defined to be g1^g2^...^gn and let B be the event of all boys defined to be b1^b2^...^bn. Let !B be defined as the complement of all boys which is also the event of at least one girl. So here !B = !(b1^b2^...^b3) which is then !B = !b1/!b2/.../!bn. Then I tried applying Bayes Rule such that P(G|!B) = P(G^!B)/P(!B). So here is where I run into a problem, P(G^!B) = P(G^(!b1/!b2/.../!bn)) = P((G^!b1)/(G^!b2)/.../(G^!bn)) = P(!b1/!b2/.../!bn). This makes sense to me as the set of all girls intersected by the set of at least one girl should be equivalent to the set of at least 1 girl. However this would mean that P(G|!B) = P(!B)/P(!B) = 1. Obviously this is wrong but I don't understand where. Your advice is very much appreciated







share|cite|improve this question














Here is a question that I would like to dolve using set theory. I know the answer but was not able to solve it with Set Theory. The question goes as follows: a father has n children, given that the father has at least 1 daughter, what is the probability of n daughters?
Here's my attempty using Set Theory:
Let G be the event of all girls defined to be g1^g2^...^gn and let B be the event of all boys defined to be b1^b2^...^bn. Let !B be defined as the complement of all boys which is also the event of at least one girl. So here !B = !(b1^b2^...^b3) which is then !B = !b1/!b2/.../!bn. Then I tried applying Bayes Rule such that P(G|!B) = P(G^!B)/P(!B). So here is where I run into a problem, P(G^!B) = P(G^(!b1/!b2/.../!bn)) = P((G^!b1)/(G^!b2)/.../(G^!bn)) = P(!b1/!b2/.../!bn). This makes sense to me as the set of all girls intersected by the set of at least one girl should be equivalent to the set of at least 1 girl. However this would mean that P(G|!B) = P(!B)/P(!B) = 1. Obviously this is wrong but I don't understand where. Your advice is very much appreciated









share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 20 at 9:43









Asaf Karagila♦

293k31408736




293k31408736










asked Aug 20 at 8:38









Jonathan Aguilera

11




11







  • 1




    This does not seem to have much to do with set theory ...
    – Henning Makholm
    Aug 20 at 9:34










  • The question presumes binary genders. Please formulate it in an inclusive manner.
    – joriki
    Aug 20 at 9:45












  • 1




    This does not seem to have much to do with set theory ...
    – Henning Makholm
    Aug 20 at 9:34










  • The question presumes binary genders. Please formulate it in an inclusive manner.
    – joriki
    Aug 20 at 9:45







1




1




This does not seem to have much to do with set theory ...
– Henning Makholm
Aug 20 at 9:34




This does not seem to have much to do with set theory ...
– Henning Makholm
Aug 20 at 9:34












The question presumes binary genders. Please formulate it in an inclusive manner.
– joriki
Aug 20 at 9:45




The question presumes binary genders. Please formulate it in an inclusive manner.
– joriki
Aug 20 at 9:45















active

oldest

votes











Your Answer




StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");

StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
convertImagesToLinks: true,
noModals: false,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);








 

draft saved


draft discarded


















StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2888540%2fprobability-of-that-n-children-are-daughters-given-at-least-one-daughter-using%23new-answer', 'question_page');

);

Post as a guest



































active

oldest

votes













active

oldest

votes









active

oldest

votes






active

oldest

votes










 

draft saved


draft discarded


























 


draft saved


draft discarded














StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2888540%2fprobability-of-that-n-children-are-daughters-given-at-least-one-daughter-using%23new-answer', 'question_page');

);

Post as a guest













































































這個網誌中的熱門文章

How to combine Bézier curves to a surface?

Mutual Information Always Non-negative

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