Confuse in Probability in Discrete Mathematics about train late problem












0












$begingroup$


A student is being late to catch the morning train in 3/10 of trials. If he runs of on time he will always catch the train. If he runs of late, he gets to the station with 5 min delay after regular train departure and so he catches the train if the train is at least 5 min delayed.




  • The train is at least 5 min delayed with probability 2/5. The student is at school on time in case that the train gets to his school with delay at most 30 min.


  • Probability that the delay of the train in the city he lived in is less than 30 minutes provided student at his station got on train on time (with delay less than 5 min) is 99/100.


  • Probability that the delay of the train in that city is less than 30 minutes provided student got on train with delay more than 5 min is 97/100.



What is the probability, that student is at school on time on a day when he runs of late?



I have read this problem for many time but i still can't figure out how to solve it, there are many infomation and it make me confuse, i don't know where to start and which infomation that i should be focus on.



Please show steps in how you solve it.










share|cite|improve this question











$endgroup$












  • $begingroup$
    Hello and welcome to Mathematics SE. Can you show us what you have tried so far? It might help you to make a flowchart with scenarios. So start with is the student late or not. Then if he is delayed, is the train delayed or not? And so on. This will help you get an overview and likely allows you to solve the problem without giving away the solution.
    $endgroup$
    – Jan
    Dec 9 '18 at 20:59










  • $begingroup$
    So the problem ask me to count the probability that the student can be at school on time on the day he runs of late, so: - If the student runs of late he will have 2/5 change to get on train. - Students can get to school on time if the train can not be delay more than 30 min: + The student will have 1/100 chance to get on train and get to school on time if the train is delay less than 5 min. + The student will have 3/100 chance to get on train and get to school on time if the train is delay more than 5 min. After all, i really confuse and don't know how to connect these data together
    $endgroup$
    – Hieu Ng
    Dec 9 '18 at 22:13










  • $begingroup$
    It seems that the conditions after '+'s are in mess, they should be about train delay at least 30 minutes.
    $endgroup$
    – Alex Ravsky
    Dec 11 '18 at 18:29
















0












$begingroup$


A student is being late to catch the morning train in 3/10 of trials. If he runs of on time he will always catch the train. If he runs of late, he gets to the station with 5 min delay after regular train departure and so he catches the train if the train is at least 5 min delayed.




  • The train is at least 5 min delayed with probability 2/5. The student is at school on time in case that the train gets to his school with delay at most 30 min.


  • Probability that the delay of the train in the city he lived in is less than 30 minutes provided student at his station got on train on time (with delay less than 5 min) is 99/100.


  • Probability that the delay of the train in that city is less than 30 minutes provided student got on train with delay more than 5 min is 97/100.



What is the probability, that student is at school on time on a day when he runs of late?



I have read this problem for many time but i still can't figure out how to solve it, there are many infomation and it make me confuse, i don't know where to start and which infomation that i should be focus on.



Please show steps in how you solve it.










share|cite|improve this question











$endgroup$












  • $begingroup$
    Hello and welcome to Mathematics SE. Can you show us what you have tried so far? It might help you to make a flowchart with scenarios. So start with is the student late or not. Then if he is delayed, is the train delayed or not? And so on. This will help you get an overview and likely allows you to solve the problem without giving away the solution.
    $endgroup$
    – Jan
    Dec 9 '18 at 20:59










  • $begingroup$
    So the problem ask me to count the probability that the student can be at school on time on the day he runs of late, so: - If the student runs of late he will have 2/5 change to get on train. - Students can get to school on time if the train can not be delay more than 30 min: + The student will have 1/100 chance to get on train and get to school on time if the train is delay less than 5 min. + The student will have 3/100 chance to get on train and get to school on time if the train is delay more than 5 min. After all, i really confuse and don't know how to connect these data together
    $endgroup$
    – Hieu Ng
    Dec 9 '18 at 22:13










  • $begingroup$
    It seems that the conditions after '+'s are in mess, they should be about train delay at least 30 minutes.
    $endgroup$
    – Alex Ravsky
    Dec 11 '18 at 18:29














0












0








0





$begingroup$


A student is being late to catch the morning train in 3/10 of trials. If he runs of on time he will always catch the train. If he runs of late, he gets to the station with 5 min delay after regular train departure and so he catches the train if the train is at least 5 min delayed.




  • The train is at least 5 min delayed with probability 2/5. The student is at school on time in case that the train gets to his school with delay at most 30 min.


  • Probability that the delay of the train in the city he lived in is less than 30 minutes provided student at his station got on train on time (with delay less than 5 min) is 99/100.


  • Probability that the delay of the train in that city is less than 30 minutes provided student got on train with delay more than 5 min is 97/100.



What is the probability, that student is at school on time on a day when he runs of late?



I have read this problem for many time but i still can't figure out how to solve it, there are many infomation and it make me confuse, i don't know where to start and which infomation that i should be focus on.



Please show steps in how you solve it.










share|cite|improve this question











$endgroup$




A student is being late to catch the morning train in 3/10 of trials. If he runs of on time he will always catch the train. If he runs of late, he gets to the station with 5 min delay after regular train departure and so he catches the train if the train is at least 5 min delayed.




  • The train is at least 5 min delayed with probability 2/5. The student is at school on time in case that the train gets to his school with delay at most 30 min.


  • Probability that the delay of the train in the city he lived in is less than 30 minutes provided student at his station got on train on time (with delay less than 5 min) is 99/100.


  • Probability that the delay of the train in that city is less than 30 minutes provided student got on train with delay more than 5 min is 97/100.



What is the probability, that student is at school on time on a day when he runs of late?



I have read this problem for many time but i still can't figure out how to solve it, there are many infomation and it make me confuse, i don't know where to start and which infomation that i should be focus on.



Please show steps in how you solve it.







probability discrete-mathematics






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 11 '18 at 18:30









Alex Ravsky

40.4k32282




40.4k32282










asked Dec 9 '18 at 20:57









Hieu NgHieu Ng

1




1












  • $begingroup$
    Hello and welcome to Mathematics SE. Can you show us what you have tried so far? It might help you to make a flowchart with scenarios. So start with is the student late or not. Then if he is delayed, is the train delayed or not? And so on. This will help you get an overview and likely allows you to solve the problem without giving away the solution.
    $endgroup$
    – Jan
    Dec 9 '18 at 20:59










  • $begingroup$
    So the problem ask me to count the probability that the student can be at school on time on the day he runs of late, so: - If the student runs of late he will have 2/5 change to get on train. - Students can get to school on time if the train can not be delay more than 30 min: + The student will have 1/100 chance to get on train and get to school on time if the train is delay less than 5 min. + The student will have 3/100 chance to get on train and get to school on time if the train is delay more than 5 min. After all, i really confuse and don't know how to connect these data together
    $endgroup$
    – Hieu Ng
    Dec 9 '18 at 22:13










  • $begingroup$
    It seems that the conditions after '+'s are in mess, they should be about train delay at least 30 minutes.
    $endgroup$
    – Alex Ravsky
    Dec 11 '18 at 18:29


















  • $begingroup$
    Hello and welcome to Mathematics SE. Can you show us what you have tried so far? It might help you to make a flowchart with scenarios. So start with is the student late or not. Then if he is delayed, is the train delayed or not? And so on. This will help you get an overview and likely allows you to solve the problem without giving away the solution.
    $endgroup$
    – Jan
    Dec 9 '18 at 20:59










  • $begingroup$
    So the problem ask me to count the probability that the student can be at school on time on the day he runs of late, so: - If the student runs of late he will have 2/5 change to get on train. - Students can get to school on time if the train can not be delay more than 30 min: + The student will have 1/100 chance to get on train and get to school on time if the train is delay less than 5 min. + The student will have 3/100 chance to get on train and get to school on time if the train is delay more than 5 min. After all, i really confuse and don't know how to connect these data together
    $endgroup$
    – Hieu Ng
    Dec 9 '18 at 22:13










  • $begingroup$
    It seems that the conditions after '+'s are in mess, they should be about train delay at least 30 minutes.
    $endgroup$
    – Alex Ravsky
    Dec 11 '18 at 18:29
















$begingroup$
Hello and welcome to Mathematics SE. Can you show us what you have tried so far? It might help you to make a flowchart with scenarios. So start with is the student late or not. Then if he is delayed, is the train delayed or not? And so on. This will help you get an overview and likely allows you to solve the problem without giving away the solution.
$endgroup$
– Jan
Dec 9 '18 at 20:59




$begingroup$
Hello and welcome to Mathematics SE. Can you show us what you have tried so far? It might help you to make a flowchart with scenarios. So start with is the student late or not. Then if he is delayed, is the train delayed or not? And so on. This will help you get an overview and likely allows you to solve the problem without giving away the solution.
$endgroup$
– Jan
Dec 9 '18 at 20:59












$begingroup$
So the problem ask me to count the probability that the student can be at school on time on the day he runs of late, so: - If the student runs of late he will have 2/5 change to get on train. - Students can get to school on time if the train can not be delay more than 30 min: + The student will have 1/100 chance to get on train and get to school on time if the train is delay less than 5 min. + The student will have 3/100 chance to get on train and get to school on time if the train is delay more than 5 min. After all, i really confuse and don't know how to connect these data together
$endgroup$
– Hieu Ng
Dec 9 '18 at 22:13




$begingroup$
So the problem ask me to count the probability that the student can be at school on time on the day he runs of late, so: - If the student runs of late he will have 2/5 change to get on train. - Students can get to school on time if the train can not be delay more than 30 min: + The student will have 1/100 chance to get on train and get to school on time if the train is delay less than 5 min. + The student will have 3/100 chance to get on train and get to school on time if the train is delay more than 5 min. After all, i really confuse and don't know how to connect these data together
$endgroup$
– Hieu Ng
Dec 9 '18 at 22:13












$begingroup$
It seems that the conditions after '+'s are in mess, they should be about train delay at least 30 minutes.
$endgroup$
– Alex Ravsky
Dec 11 '18 at 18:29




$begingroup$
It seems that the conditions after '+'s are in mess, they should be about train delay at least 30 minutes.
$endgroup$
– Alex Ravsky
Dec 11 '18 at 18:29










1 Answer
1






active

oldest

votes


















0












$begingroup$


What is the probability, that student is at school on time on a day when he runs of late?




Maybe the problem author wanted to put a complex idea in it, but I see only the following simple scenario. This unlucky day was happened. The student is late. So there is no use to think what could happen if he was in time. It already gone. He have to think about future. At the first, he have to catch the train. “He catches the train if the train is at least 5 min delayed”. “The train is at least 5 min delayed with probability 2/5”. So probability of the success at the first step is $2/5$. The second step is that the delay of the train is less than 30 minutes. Since student got on train with delay more than 5 min, probability of the success at the second step is $97/100$. So the total success probability is $(2/5)(97/100)=97/250$.






share|cite|improve this answer









$endgroup$









  • 1




    $begingroup$
    Thank you so much, i think i should think more simple about this problem.
    $endgroup$
    – Hieu Ng
    Dec 17 '18 at 7:21











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%2f3032998%2fconfuse-in-probability-in-discrete-mathematics-about-train-late-problem%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









0












$begingroup$


What is the probability, that student is at school on time on a day when he runs of late?




Maybe the problem author wanted to put a complex idea in it, but I see only the following simple scenario. This unlucky day was happened. The student is late. So there is no use to think what could happen if he was in time. It already gone. He have to think about future. At the first, he have to catch the train. “He catches the train if the train is at least 5 min delayed”. “The train is at least 5 min delayed with probability 2/5”. So probability of the success at the first step is $2/5$. The second step is that the delay of the train is less than 30 minutes. Since student got on train with delay more than 5 min, probability of the success at the second step is $97/100$. So the total success probability is $(2/5)(97/100)=97/250$.






share|cite|improve this answer









$endgroup$









  • 1




    $begingroup$
    Thank you so much, i think i should think more simple about this problem.
    $endgroup$
    – Hieu Ng
    Dec 17 '18 at 7:21
















0












$begingroup$


What is the probability, that student is at school on time on a day when he runs of late?




Maybe the problem author wanted to put a complex idea in it, but I see only the following simple scenario. This unlucky day was happened. The student is late. So there is no use to think what could happen if he was in time. It already gone. He have to think about future. At the first, he have to catch the train. “He catches the train if the train is at least 5 min delayed”. “The train is at least 5 min delayed with probability 2/5”. So probability of the success at the first step is $2/5$. The second step is that the delay of the train is less than 30 minutes. Since student got on train with delay more than 5 min, probability of the success at the second step is $97/100$. So the total success probability is $(2/5)(97/100)=97/250$.






share|cite|improve this answer









$endgroup$









  • 1




    $begingroup$
    Thank you so much, i think i should think more simple about this problem.
    $endgroup$
    – Hieu Ng
    Dec 17 '18 at 7:21














0












0








0





$begingroup$


What is the probability, that student is at school on time on a day when he runs of late?




Maybe the problem author wanted to put a complex idea in it, but I see only the following simple scenario. This unlucky day was happened. The student is late. So there is no use to think what could happen if he was in time. It already gone. He have to think about future. At the first, he have to catch the train. “He catches the train if the train is at least 5 min delayed”. “The train is at least 5 min delayed with probability 2/5”. So probability of the success at the first step is $2/5$. The second step is that the delay of the train is less than 30 minutes. Since student got on train with delay more than 5 min, probability of the success at the second step is $97/100$. So the total success probability is $(2/5)(97/100)=97/250$.






share|cite|improve this answer









$endgroup$




What is the probability, that student is at school on time on a day when he runs of late?




Maybe the problem author wanted to put a complex idea in it, but I see only the following simple scenario. This unlucky day was happened. The student is late. So there is no use to think what could happen if he was in time. It already gone. He have to think about future. At the first, he have to catch the train. “He catches the train if the train is at least 5 min delayed”. “The train is at least 5 min delayed with probability 2/5”. So probability of the success at the first step is $2/5$. The second step is that the delay of the train is less than 30 minutes. Since student got on train with delay more than 5 min, probability of the success at the second step is $97/100$. So the total success probability is $(2/5)(97/100)=97/250$.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Dec 11 '18 at 18:26









Alex RavskyAlex Ravsky

40.4k32282




40.4k32282








  • 1




    $begingroup$
    Thank you so much, i think i should think more simple about this problem.
    $endgroup$
    – Hieu Ng
    Dec 17 '18 at 7:21














  • 1




    $begingroup$
    Thank you so much, i think i should think more simple about this problem.
    $endgroup$
    – Hieu Ng
    Dec 17 '18 at 7:21








1




1




$begingroup$
Thank you so much, i think i should think more simple about this problem.
$endgroup$
– Hieu Ng
Dec 17 '18 at 7:21




$begingroup$
Thank you so much, i think i should think more simple about this problem.
$endgroup$
– Hieu Ng
Dec 17 '18 at 7:21


















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%2f3032998%2fconfuse-in-probability-in-discrete-mathematics-about-train-late-problem%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

Ellipse (mathématiques)

Quarter-circle Tiles

Mont Emei