In a hand of bridge what is the probability that you have 5 spades and your partner has remaining 8.












2












$begingroup$


I am a complete noob in playing cards. Please help me out in this problem and also explain me the concept behind the bridge card game.






probability







share|cite|improve this question









$endgroup$








  • 2




    $begingroup$
    All you need to know is that there are $52$ cards, $13$ of which are spades; you have $13$ of the cards and your partner has another $13$.
    $endgroup$
    – Misha Lavrov
    Jan 25 at 16:47










  • $begingroup$
    Thanks. It helped me to write the answer.
    $endgroup$
    – Abhishek Ghosh
    Jan 25 at 16:56
















2












$begingroup$


I am a complete noob in playing cards. Please help me out in this problem and also explain me the concept behind the bridge card game.






probability







share|cite|improve this question









$endgroup$








  • 2




    $begingroup$
    All you need to know is that there are $52$ cards, $13$ of which are spades; you have $13$ of the cards and your partner has another $13$.
    $endgroup$
    – Misha Lavrov
    Jan 25 at 16:47










  • $begingroup$
    Thanks. It helped me to write the answer.
    $endgroup$
    – Abhishek Ghosh
    Jan 25 at 16:56














2












2








2





$begingroup$


I am a complete noob in playing cards. Please help me out in this problem and also explain me the concept behind the bridge card game.






probability







share|cite|improve this question









$endgroup$




I am a complete noob in playing cards. Please help me out in this problem and also explain me the concept behind the bridge card game.






probability




probability






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Jan 25 at 16:44









Abhishek GhoshAbhishek Ghosh

878




878








  • 2




    $begingroup$
    All you need to know is that there are $52$ cards, $13$ of which are spades; you have $13$ of the cards and your partner has another $13$.
    $endgroup$
    – Misha Lavrov
    Jan 25 at 16:47










  • $begingroup$
    Thanks. It helped me to write the answer.
    $endgroup$
    – Abhishek Ghosh
    Jan 25 at 16:56














  • 2




    $begingroup$
    All you need to know is that there are $52$ cards, $13$ of which are spades; you have $13$ of the cards and your partner has another $13$.
    $endgroup$
    – Misha Lavrov
    Jan 25 at 16:47










  • $begingroup$
    Thanks. It helped me to write the answer.
    $endgroup$
    – Abhishek Ghosh
    Jan 25 at 16:56








2




2




$begingroup$
All you need to know is that there are $52$ cards, $13$ of which are spades; you have $13$ of the cards and your partner has another $13$.
$endgroup$
– Misha Lavrov
Jan 25 at 16:47




$begingroup$
All you need to know is that there are $52$ cards, $13$ of which are spades; you have $13$ of the cards and your partner has another $13$.
$endgroup$
– Misha Lavrov
Jan 25 at 16:47












$begingroup$
Thanks. It helped me to write the answer.
$endgroup$
– Abhishek Ghosh
Jan 25 at 16:56




$begingroup$
Thanks. It helped me to write the answer.
$endgroup$
– Abhishek Ghosh
Jan 25 at 16:56










1 Answer
1






active

oldest

votes


















2












$begingroup$

So you should be having $13$ cards out of which $5$ are spades and your partner also has $13$ cards out of which $8$ are spades.



So total number of favourable outcomes $m=binom{13}{5}timesbinom{39}{8}timesbinom{31}{5}$



The total number of possible outcomes $n=binom{52}{13}timesbinom{39}{13}$



Required probability $=frac{m}{n}approx2.608399419times10^{-6}$






share|cite|improve this answer











$endgroup$









  • 1




    $begingroup$
    This is correct, however for completeness and transparency it helps to explain how each result is formed. (e.g. pick the spades used for your hand, pick remaining cards for your hand, pick non-spades for partner's hand).
    $endgroup$
    – JMoravitz
    Jan 25 at 17:18











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',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
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%2f3087310%2fin-a-hand-of-bridge-what-is-the-probability-that-you-have-5-spades-and-your-part%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown

























1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









2












$begingroup$

So you should be having $13$ cards out of which $5$ are spades and your partner also has $13$ cards out of which $8$ are spades.



So total number of favourable outcomes $m=binom{13}{5}timesbinom{39}{8}timesbinom{31}{5}$



The total number of possible outcomes $n=binom{52}{13}timesbinom{39}{13}$



Required probability $=frac{m}{n}approx2.608399419times10^{-6}$






share|cite|improve this answer











$endgroup$









  • 1




    $begingroup$
    This is correct, however for completeness and transparency it helps to explain how each result is formed. (e.g. pick the spades used for your hand, pick remaining cards for your hand, pick non-spades for partner's hand).
    $endgroup$
    – JMoravitz
    Jan 25 at 17:18
















2












$begingroup$

So you should be having $13$ cards out of which $5$ are spades and your partner also has $13$ cards out of which $8$ are spades.



So total number of favourable outcomes $m=binom{13}{5}timesbinom{39}{8}timesbinom{31}{5}$



The total number of possible outcomes $n=binom{52}{13}timesbinom{39}{13}$



Required probability $=frac{m}{n}approx2.608399419times10^{-6}$






share|cite|improve this answer











$endgroup$









  • 1




    $begingroup$
    This is correct, however for completeness and transparency it helps to explain how each result is formed. (e.g. pick the spades used for your hand, pick remaining cards for your hand, pick non-spades for partner's hand).
    $endgroup$
    – JMoravitz
    Jan 25 at 17:18














2












2








2





$begingroup$

So you should be having $13$ cards out of which $5$ are spades and your partner also has $13$ cards out of which $8$ are spades.



So total number of favourable outcomes $m=binom{13}{5}timesbinom{39}{8}timesbinom{31}{5}$



The total number of possible outcomes $n=binom{52}{13}timesbinom{39}{13}$



Required probability $=frac{m}{n}approx2.608399419times10^{-6}$






share|cite|improve this answer











$endgroup$



So you should be having $13$ cards out of which $5$ are spades and your partner also has $13$ cards out of which $8$ are spades.



So total number of favourable outcomes $m=binom{13}{5}timesbinom{39}{8}timesbinom{31}{5}$



The total number of possible outcomes $n=binom{52}{13}timesbinom{39}{13}$



Required probability $=frac{m}{n}approx2.608399419times10^{-6}$







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Jan 25 at 17:12









Daniel Mathias

1,36018




1,36018










answered Jan 25 at 16:55









Abhishek GhoshAbhishek Ghosh

878




878








  • 1




    $begingroup$
    This is correct, however for completeness and transparency it helps to explain how each result is formed. (e.g. pick the spades used for your hand, pick remaining cards for your hand, pick non-spades for partner's hand).
    $endgroup$
    – JMoravitz
    Jan 25 at 17:18














  • 1




    $begingroup$
    This is correct, however for completeness and transparency it helps to explain how each result is formed. (e.g. pick the spades used for your hand, pick remaining cards for your hand, pick non-spades for partner's hand).
    $endgroup$
    – JMoravitz
    Jan 25 at 17:18








1




1




$begingroup$
This is correct, however for completeness and transparency it helps to explain how each result is formed. (e.g. pick the spades used for your hand, pick remaining cards for your hand, pick non-spades for partner's hand).
$endgroup$
– JMoravitz
Jan 25 at 17:18




$begingroup$
This is correct, however for completeness and transparency it helps to explain how each result is formed. (e.g. pick the spades used for your hand, pick remaining cards for your hand, pick non-spades for partner's hand).
$endgroup$
– JMoravitz
Jan 25 at 17:18


















draft saved

draft discarded




















































Thanks for contributing an answer to Mathematics Stack Exchange!


  • Please be sure to answer the question. Provide details and share your research!

But avoid …



  • Asking for help, clarification, or responding to other answers.

  • Making statements based on opinion; back them up with references or personal experience.


Use MathJax to format equations. MathJax reference.


To learn more, see our tips on writing great answers.




draft saved


draft discarded














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3087310%2fin-a-hand-of-bridge-what-is-the-probability-that-you-have-5-spades-and-your-part%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown





















































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown

































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown







Popular posts from this blog

MongoDB - Not Authorized To Execute Command

Image
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty{ height:90px;width:728px;box-sizing:border-box; } 0 I have successfully enabled authorization on MongoDB and I have created an account on the admin database and then I created an account for my database called test. The following connection string to connect to my test database works successfully: mongo --host 192.168.17.52 --port 27017 -u user1 -p password --authenticationDatabase test Only problem I have now is, I cannot execute commands such as: show dbs. I get the following error when I try to do so: "errmsg" : "not authorized on admin to execute command { listDatabases: 1.0, lsid: { id: UUID("a1d5bc0d-bc58-485e-b232-270758a89455") }, $db: "admin...
Read more

Npm cannot find a required file even through it is in the searched directory

Image
up vote 0 down vote favorite I got that error: users-Air:pdfuploader user$ npm run start client@0.1.0 start /Users/user/Documents/pdfuploader react-scripts start Could not find a required file. Name: index.html Searched in: /Users/user/Documents/pdfuploader/public npm ERR! code ELIFECYCLE npm ERR! errno 1 npm ERR! client@0.1.0 start: `react-scripts start` npm ERR! Exit status 1 npm ERR! npm ERR! Failed at the client@0.1.0 start script. npm ERR! This is probably not a problem with npm. There is likely additional logging output above. npm ERR! A complete log of this run can be found in: npm ERR! /Users/user/.npm/_logs/2018-11-19T10_19_14_555Z-debug.log users-Air:pdfuploader user$ And the file is in /Users/user/Documents/pdfuploader/public as you can see in my github repository: https://github.c...
Read more

in spring boot 2.1 many test slices are not allowed anymore due to multiple @BootstrapWith

Image
1 I tried to upgrade a yummy sandwich made of two test slices (@JsonTest and @JdbcTest in my case, crunchy test code in between) adding spring boot 2.1 flavour to it. But it seems it was not much of a success. I cannot annotate my tests with many @...Test since they are now each bringing their own XxxTestContextBootstrapper. It used to work when they all used same SpringBootTestContextBootstrapper. @RunWith(SpringRunner.class) @JdbcTest @JsonTest public class Test { @Test public void test() { System.out.printn("Hello, World !"); } } The error I get from BootstrapUtils is illegalStateException : Configuration error: found multiple declarations of @BootstrapWith for test class I understand I might be doing something wrong here but is there an easy way I could load both Json and Jdbc contex...
Read more