$5$ prizes are distributed among $20$ students. What is the probability that a particular student receives...
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There are $5$ prizes that are to be distributed among $20$ students. What is the probability that a particular student receives $3$ prizes ?
probability combinatorics
edited Dec 13 '18 at 7:12
heropup
63.8k762102
asked Dec 13 '18 at 5:40
George W. SmithGeorge W. Smith
4
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closed as off-topic by Chase Ryan Taylor, Brahadeesh, heropup, Cesareo, José Carlos Santos Dec 13 '18 at 9:30
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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Chase Ryan Taylor, Brahadeesh, heropup, Cesareo, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
There are $5$ prizes that are to be distributed among $20$ students. What is the probability that a particular student receives $3$ prizes ?
probability combinatorics
edited Dec 13 '18 at 7:12
heropup
63.8k762102
asked Dec 13 '18 at 5:40
George W. SmithGeorge W. Smith
4
$endgroup$
closed as off-topic by Chase Ryan Taylor, Brahadeesh, heropup, Cesareo, José Carlos Santos Dec 13 '18 at 9:30
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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Chase Ryan Taylor, Brahadeesh, heropup, Cesareo, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
How do you propose to start with the answer? Find the number of total outcomes first, since you are dealing with probability. Do you know the number of total outcomes?
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– астон вілла олоф мэллбэрг
Dec 13 '18 at 5:51
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Depends on how they are distributed. Is it a lottery? Is there a jury that picks the winners based on who they like most? Or on how the students perform on a test? Does the jury give out one prize first and then choose the winner of the second prize only among the 19 students that do not yet have a prize, or among all 20? Does already having the first prize increase the probability of receiving the second prize since it is an easy to measure signal that the student apparently deserves prizes? It seems that all these scenarios are pretty common in the real world but they yield different answers
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– Vincent
Dec 13 '18 at 8:36
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Also, does "a particular student receives 3 prizes" mean "a particular student receives exactly 3 prizes" or "a particular student receives at least 3 prizes"?
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– Yanior Weg
Dec 13 '18 at 9:25
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It was closed a few seconds before I copy and paste my answer ...
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– Damien
Dec 13 '18 at 9:48
$begingroup$
Note: for the same scenario, I got a result different from the one provided in the only answer
$endgroup$
– Damien
Dec 13 '18 at 13:32
add a comment |
$begingroup$
There are $5$ prizes that are to be distributed among $20$ students. What is the probability that a particular student receives $3$ prizes ?
probability combinatorics
edited Dec 13 '18 at 7:12
heropup
63.8k762102
asked Dec 13 '18 at 5:40
George W. SmithGeorge W. Smith
4
$endgroup$
There are $5$ prizes that are to be distributed among $20$ students. What is the probability that a particular student receives $3$ prizes ?
probability combinatorics
probability combinatorics
edited Dec 13 '18 at 7:12
heropup
63.8k762102
asked Dec 13 '18 at 5:40
George W. SmithGeorge W. Smith
4
edited Dec 13 '18 at 7:12
heropup
63.8k762102
asked Dec 13 '18 at 5:40
George W. SmithGeorge W. Smith
4
edited Dec 13 '18 at 7:12
heropup
63.8k762102
edited Dec 13 '18 at 7:12
heropup
63.8k762102
edited Dec 13 '18 at 7:12
heropup
63.8k762102
63.8k762102
asked Dec 13 '18 at 5:40
George W. SmithGeorge W. Smith
4
asked Dec 13 '18 at 5:40
George W. SmithGeorge W. Smith
4
asked Dec 13 '18 at 5:40
George W. SmithGeorge W. Smith
4
4
closed as off-topic by Chase Ryan Taylor, Brahadeesh, heropup, Cesareo, José Carlos Santos Dec 13 '18 at 9:30
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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Chase Ryan Taylor, Brahadeesh, heropup, Cesareo, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Chase Ryan Taylor, Brahadeesh, heropup, Cesareo, José Carlos Santos Dec 13 '18 at 9:30
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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Chase Ryan Taylor, Brahadeesh, heropup, Cesareo, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
How do you propose to start with the answer? Find the number of total outcomes first, since you are dealing with probability. Do you know the number of total outcomes?
$endgroup$
– астон вілла олоф мэллбэрг
Dec 13 '18 at 5:51
$begingroup$
Depends on how they are distributed. Is it a lottery? Is there a jury that picks the winners based on who they like most? Or on how the students perform on a test? Does the jury give out one prize first and then choose the winner of the second prize only among the 19 students that do not yet have a prize, or among all 20? Does already having the first prize increase the probability of receiving the second prize since it is an easy to measure signal that the student apparently deserves prizes? It seems that all these scenarios are pretty common in the real world but they yield different answers
$endgroup$
– Vincent
Dec 13 '18 at 8:36
$begingroup$
Also, does "a particular student receives 3 prizes" mean "a particular student receives exactly 3 prizes" or "a particular student receives at least 3 prizes"?
$endgroup$
– Yanior Weg
Dec 13 '18 at 9:25
$begingroup$
It was closed a few seconds before I copy and paste my answer ...
$endgroup$
– Damien
Dec 13 '18 at 9:48
$begingroup$
Note: for the same scenario, I got a result different from the one provided in the only answer
$endgroup$
– Damien
Dec 13 '18 at 13:32
add a comment |
$begingroup$
How do you propose to start with the answer? Find the number of total outcomes first, since you are dealing with probability. Do you know the number of total outcomes?
$endgroup$
– астон вілла олоф мэллбэрг
Dec 13 '18 at 5:51
$begingroup$
Depends on how they are distributed. Is it a lottery? Is there a jury that picks the winners based on who they like most? Or on how the students perform on a test? Does the jury give out one prize first and then choose the winner of the second prize only among the 19 students that do not yet have a prize, or among all 20? Does already having the first prize increase the probability of receiving the second prize since it is an easy to measure signal that the student apparently deserves prizes? It seems that all these scenarios are pretty common in the real world but they yield different answers
$endgroup$
– Vincent
Dec 13 '18 at 8:36
$begingroup$
Also, does "a particular student receives 3 prizes" mean "a particular student receives exactly 3 prizes" or "a particular student receives at least 3 prizes"?
$endgroup$
– Yanior Weg
Dec 13 '18 at 9:25
$begingroup$
It was closed a few seconds before I copy and paste my answer ...
$endgroup$
– Damien
Dec 13 '18 at 9:48
$begingroup$
Note: for the same scenario, I got a result different from the one provided in the only answer
$endgroup$
– Damien
Dec 13 '18 at 13:32
$begingroup$
How do you propose to start with the answer? Find the number of total outcomes first, since you are dealing with probability. Do you know the number of total outcomes?
$endgroup$
– астон вілла олоф мэллбэрг
Dec 13 '18 at 5:51
$begingroup$
How do you propose to start with the answer? Find the number of total outcomes first, since you are dealing with probability. Do you know the number of total outcomes?
$endgroup$
– астон вілла олоф мэллбэрг
Dec 13 '18 at 5:51
$begingroup$
Depends on how they are distributed. Is it a lottery? Is there a jury that picks the winners based on who they like most? Or on how the students perform on a test? Does the jury give out one prize first and then choose the winner of the second prize only among the 19 students that do not yet have a prize, or among all 20? Does already having the first prize increase the probability of receiving the second prize since it is an easy to measure signal that the student apparently deserves prizes? It seems that all these scenarios are pretty common in the real world but they yield different answers
$endgroup$
– Vincent
Dec 13 '18 at 8:36
$begingroup$
Depends on how they are distributed. Is it a lottery? Is there a jury that picks the winners based on who they like most? Or on how the students perform on a test? Does the jury give out one prize first and then choose the winner of the second prize only among the 19 students that do not yet have a prize, or among all 20? Does already having the first prize increase the probability of receiving the second prize since it is an easy to measure signal that the student apparently deserves prizes? It seems that all these scenarios are pretty common in the real world but they yield different answers
$endgroup$
– Vincent
Dec 13 '18 at 8:36
$begingroup$
Also, does "a particular student receives 3 prizes" mean "a particular student receives exactly 3 prizes" or "a particular student receives at least 3 prizes"?
$endgroup$
– Yanior Weg
Dec 13 '18 at 9:25
$begingroup$
Also, does "a particular student receives 3 prizes" mean "a particular student receives exactly 3 prizes" or "a particular student receives at least 3 prizes"?
$endgroup$
– Yanior Weg
Dec 13 '18 at 9:25
$begingroup$
It was closed a few seconds before I copy and paste my answer ...
$endgroup$
– Damien
Dec 13 '18 at 9:48
$begingroup$
It was closed a few seconds before I copy and paste my answer ...
$endgroup$
– Damien
Dec 13 '18 at 9:48
$begingroup$
Note: for the same scenario, I got a result different from the one provided in the only answer
$endgroup$
– Damien
Dec 13 '18 at 13:32
$begingroup$
Note: for the same scenario, I got a result different from the one provided in the only answer
$endgroup$
– Damien
Dec 13 '18 at 13:32
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Assuming prizes are uniques, each can be given out in $20$ ways. So total number of ways of distributing $5$ orizes is
$$N = 20^5$$
Now one person needs to get $3$ prizes. So we select three of them out in $5choose3$ ways and bundle them together. This bundle can go to any student. This gives us
$$n={5choose3}cdot20 = 200$$
Now the other two prizes can go to any of the $19$ students left in $19$ ways each. So total is
$$n = 200cdot19cdot19=72200$$
Hence probability is
$$P=frac{72200}{20^5}=0.0225625$$
answered Dec 13 '18 at 5:54
Sauhard SharmaSauhard Sharma
953318
$endgroup$
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Assuming prizes are uniques, each can be given out in $20$ ways. So total number of ways of distributing $5$ orizes is
$$N = 20^5$$
Now one person needs to get $3$ prizes. So we select three of them out in $5choose3$ ways and bundle them together. This bundle can go to any student. This gives us
$$n={5choose3}cdot20 = 200$$
Now the other two prizes can go to any of the $19$ students left in $19$ ways each. So total is
$$n = 200cdot19cdot19=72200$$
Hence probability is
$$P=frac{72200}{20^5}=0.0225625$$
answered Dec 13 '18 at 5:54
Sauhard SharmaSauhard Sharma
953318
$endgroup$
add a comment |
$begingroup$
Assuming prizes are uniques, each can be given out in $20$ ways. So total number of ways of distributing $5$ orizes is
$$N = 20^5$$
Now one person needs to get $3$ prizes. So we select three of them out in $5choose3$ ways and bundle them together. This bundle can go to any student. This gives us
$$n={5choose3}cdot20 = 200$$
Now the other two prizes can go to any of the $19$ students left in $19$ ways each. So total is
$$n = 200cdot19cdot19=72200$$
Hence probability is
$$P=frac{72200}{20^5}=0.0225625$$
answered Dec 13 '18 at 5:54
Sauhard SharmaSauhard Sharma
953318
$endgroup$
add a comment |
$begingroup$
Assuming prizes are uniques, each can be given out in $20$ ways. So total number of ways of distributing $5$ orizes is
$$N = 20^5$$
Now one person needs to get $3$ prizes. So we select three of them out in $5choose3$ ways and bundle them together. This bundle can go to any student. This gives us
$$n={5choose3}cdot20 = 200$$
Now the other two prizes can go to any of the $19$ students left in $19$ ways each. So total is
$$n = 200cdot19cdot19=72200$$
Hence probability is
$$P=frac{72200}{20^5}=0.0225625$$
answered Dec 13 '18 at 5:54
Sauhard SharmaSauhard Sharma
953318
$endgroup$
Assuming prizes are uniques, each can be given out in $20$ ways. So total number of ways of distributing $5$ orizes is
$$N = 20^5$$
Now one person needs to get $3$ prizes. So we select three of them out in $5choose3$ ways and bundle them together. This bundle can go to any student. This gives us
$$n={5choose3}cdot20 = 200$$
Now the other two prizes can go to any of the $19$ students left in $19$ ways each. So total is
$$n = 200cdot19cdot19=72200$$
Hence probability is
$$P=frac{72200}{20^5}=0.0225625$$
answered Dec 13 '18 at 5:54
Sauhard SharmaSauhard Sharma
953318
answered Dec 13 '18 at 5:54
Sauhard SharmaSauhard Sharma
953318
answered Dec 13 '18 at 5:54
Sauhard SharmaSauhard Sharma
953318
answered Dec 13 '18 at 5:54
Sauhard SharmaSauhard Sharma
953318
953318
add a comment |
add a comment |
$begingroup$
How do you propose to start with the answer? Find the number of total outcomes first, since you are dealing with probability. Do you know the number of total outcomes?
$endgroup$
– астон вілла олоф мэллбэрг
Dec 13 '18 at 5:51
$begingroup$
Depends on how they are distributed. Is it a lottery? Is there a jury that picks the winners based on who they like most? Or on how the students perform on a test? Does the jury give out one prize first and then choose the winner of the second prize only among the 19 students that do not yet have a prize, or among all 20? Does already having the first prize increase the probability of receiving the second prize since it is an easy to measure signal that the student apparently deserves prizes? It seems that all these scenarios are pretty common in the real world but they yield different answers
$endgroup$
– Vincent
Dec 13 '18 at 8:36
$begingroup$
Also, does "a particular student receives 3 prizes" mean "a particular student receives exactly 3 prizes" or "a particular student receives at least 3 prizes"?
$endgroup$
– Yanior Weg
Dec 13 '18 at 9:25
$begingroup$
It was closed a few seconds before I copy and paste my answer ...
$endgroup$
– Damien
Dec 13 '18 at 9:48
$begingroup$
Note: for the same scenario, I got a result different from the one provided in the only answer
$endgroup$
– Damien
Dec 13 '18 at 13:32