Probability question at least one without replacement.












1














Title says it all, it’s a bit confusing to understand.



A bag contains 13 marbles 6 red, 3 yellow, and 4 green. If 3 marbles are chosen at random (without replacement) then what is the probability that at least one of them is yellow.



This is what I got. 1-(3/13)(2/12)(1/11).



I know that at least one is 1-p. Since it’s asking if 3 are chosen at random without replacement then what’s the probability of 3 yellow, I figured if you picked up a marble out of a bag for the first time your chance of getting a yellow marble would be 3/13 since there’s no replacement it would decrease the second time and the third. So the first chance would be 3/13 the second would be 2/12 and the third would be 1/11










share|cite|improve this question
























  • math.stackexchange.com/questions/697433/…
    – lab bhattacharjee
    Dec 4 '18 at 16:19










  • What have you tried so far?
    – user3482749
    Dec 4 '18 at 16:39










  • This is what I got. 1-(3/13)*(2/12)*(1/11). Is that correct
    – J.sant
    Dec 4 '18 at 16:41










  • I was asking for a thought process, not a number.
    – user3482749
    Dec 4 '18 at 16:51










  • Well, I know that at least one is 1-p. Since it’s asking if 3 are chosen at random without replacement then what’s the probability of 3 yellow, I figured if you picked up a marble out of a bag for the first time your chance of getting a yellow marble would be 3/13 since there’s no replacement it would decrease the second time and the third. So the first chance would be 3/13 the second would be 2/12 and the third would be 1/11
    – J.sant
    Dec 4 '18 at 16:58
















1














Title says it all, it’s a bit confusing to understand.



A bag contains 13 marbles 6 red, 3 yellow, and 4 green. If 3 marbles are chosen at random (without replacement) then what is the probability that at least one of them is yellow.



This is what I got. 1-(3/13)(2/12)(1/11).



I know that at least one is 1-p. Since it’s asking if 3 are chosen at random without replacement then what’s the probability of 3 yellow, I figured if you picked up a marble out of a bag for the first time your chance of getting a yellow marble would be 3/13 since there’s no replacement it would decrease the second time and the third. So the first chance would be 3/13 the second would be 2/12 and the third would be 1/11










share|cite|improve this question
























  • math.stackexchange.com/questions/697433/…
    – lab bhattacharjee
    Dec 4 '18 at 16:19










  • What have you tried so far?
    – user3482749
    Dec 4 '18 at 16:39










  • This is what I got. 1-(3/13)*(2/12)*(1/11). Is that correct
    – J.sant
    Dec 4 '18 at 16:41










  • I was asking for a thought process, not a number.
    – user3482749
    Dec 4 '18 at 16:51










  • Well, I know that at least one is 1-p. Since it’s asking if 3 are chosen at random without replacement then what’s the probability of 3 yellow, I figured if you picked up a marble out of a bag for the first time your chance of getting a yellow marble would be 3/13 since there’s no replacement it would decrease the second time and the third. So the first chance would be 3/13 the second would be 2/12 and the third would be 1/11
    – J.sant
    Dec 4 '18 at 16:58














1












1








1







Title says it all, it’s a bit confusing to understand.



A bag contains 13 marbles 6 red, 3 yellow, and 4 green. If 3 marbles are chosen at random (without replacement) then what is the probability that at least one of them is yellow.



This is what I got. 1-(3/13)(2/12)(1/11).



I know that at least one is 1-p. Since it’s asking if 3 are chosen at random without replacement then what’s the probability of 3 yellow, I figured if you picked up a marble out of a bag for the first time your chance of getting a yellow marble would be 3/13 since there’s no replacement it would decrease the second time and the third. So the first chance would be 3/13 the second would be 2/12 and the third would be 1/11










share|cite|improve this question















Title says it all, it’s a bit confusing to understand.



A bag contains 13 marbles 6 red, 3 yellow, and 4 green. If 3 marbles are chosen at random (without replacement) then what is the probability that at least one of them is yellow.



This is what I got. 1-(3/13)(2/12)(1/11).



I know that at least one is 1-p. Since it’s asking if 3 are chosen at random without replacement then what’s the probability of 3 yellow, I figured if you picked up a marble out of a bag for the first time your chance of getting a yellow marble would be 3/13 since there’s no replacement it would decrease the second time and the third. So the first chance would be 3/13 the second would be 2/12 and the third would be 1/11







probability combinatorics






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 4 '18 at 17:29

























asked Dec 4 '18 at 16:14









J.sant

83




83












  • math.stackexchange.com/questions/697433/…
    – lab bhattacharjee
    Dec 4 '18 at 16:19










  • What have you tried so far?
    – user3482749
    Dec 4 '18 at 16:39










  • This is what I got. 1-(3/13)*(2/12)*(1/11). Is that correct
    – J.sant
    Dec 4 '18 at 16:41










  • I was asking for a thought process, not a number.
    – user3482749
    Dec 4 '18 at 16:51










  • Well, I know that at least one is 1-p. Since it’s asking if 3 are chosen at random without replacement then what’s the probability of 3 yellow, I figured if you picked up a marble out of a bag for the first time your chance of getting a yellow marble would be 3/13 since there’s no replacement it would decrease the second time and the third. So the first chance would be 3/13 the second would be 2/12 and the third would be 1/11
    – J.sant
    Dec 4 '18 at 16:58


















  • math.stackexchange.com/questions/697433/…
    – lab bhattacharjee
    Dec 4 '18 at 16:19










  • What have you tried so far?
    – user3482749
    Dec 4 '18 at 16:39










  • This is what I got. 1-(3/13)*(2/12)*(1/11). Is that correct
    – J.sant
    Dec 4 '18 at 16:41










  • I was asking for a thought process, not a number.
    – user3482749
    Dec 4 '18 at 16:51










  • Well, I know that at least one is 1-p. Since it’s asking if 3 are chosen at random without replacement then what’s the probability of 3 yellow, I figured if you picked up a marble out of a bag for the first time your chance of getting a yellow marble would be 3/13 since there’s no replacement it would decrease the second time and the third. So the first chance would be 3/13 the second would be 2/12 and the third would be 1/11
    – J.sant
    Dec 4 '18 at 16:58
















math.stackexchange.com/questions/697433/…
– lab bhattacharjee
Dec 4 '18 at 16:19




math.stackexchange.com/questions/697433/…
– lab bhattacharjee
Dec 4 '18 at 16:19












What have you tried so far?
– user3482749
Dec 4 '18 at 16:39




What have you tried so far?
– user3482749
Dec 4 '18 at 16:39












This is what I got. 1-(3/13)*(2/12)*(1/11). Is that correct
– J.sant
Dec 4 '18 at 16:41




This is what I got. 1-(3/13)*(2/12)*(1/11). Is that correct
– J.sant
Dec 4 '18 at 16:41












I was asking for a thought process, not a number.
– user3482749
Dec 4 '18 at 16:51




I was asking for a thought process, not a number.
– user3482749
Dec 4 '18 at 16:51












Well, I know that at least one is 1-p. Since it’s asking if 3 are chosen at random without replacement then what’s the probability of 3 yellow, I figured if you picked up a marble out of a bag for the first time your chance of getting a yellow marble would be 3/13 since there’s no replacement it would decrease the second time and the third. So the first chance would be 3/13 the second would be 2/12 and the third would be 1/11
– J.sant
Dec 4 '18 at 16:58




Well, I know that at least one is 1-p. Since it’s asking if 3 are chosen at random without replacement then what’s the probability of 3 yellow, I figured if you picked up a marble out of a bag for the first time your chance of getting a yellow marble would be 3/13 since there’s no replacement it would decrease the second time and the third. So the first chance would be 3/13 the second would be 2/12 and the third would be 1/11
– J.sant
Dec 4 '18 at 16:58










1 Answer
1






active

oldest

votes


















1














HINT




  1. Find the probability that none are yellow.

  2. Remember that if $A$ is any event, then $mathbb{P}[A] = 1-mathbb{P}[bar{A}]$


UPDATE




  1. The first time you grab a yellow ball with a chance of 3/13. You want the negation of this, so the chance of that is $1-3/13 = 10/30$.

  2. The second time, you grab a yellow (assuming first time you did not) with a chance 3/12. Third time it will be 3/11.

  3. You want to draw yellow in neither of the tries, the probability of that is $$
    left[1 - frac{3}{13}right]
    times left[1 - frac{3}{12}right]
    times left[1 - frac{3}{11}right]
    = frac{10 cdot 9 cdot 8}{13 cdot 12 cdot 11}
    = frac{60}{143}
    $$


  4. Finally you want the probability that any draw results in a yellow, which is $$1 - frac{60}{143} = frac{83}{143} approx 58%.$$






share|cite|improve this answer























  • This is what I got. 1-(3/13)*(2/12)*(1/11). Is that correct?
    – J.sant
    Dec 4 '18 at 16:35








  • 1




    @J.sant No, you have to calculate $1-P("color{blue}{textrm{No yellow}} textrm{marble is chosen}")$. The probability is approximately $58%$
    – callculus
    Dec 4 '18 at 17:35








  • 1




    So 1-10/13. That’s the probability of none yellow. Is that correct?
    – J.sant
    Dec 4 '18 at 18:22








  • 1




    @J.sant Not really. You chose your first non-yellow marble: $frac{10}{13}$. Then you choose your second non-yellow marble: $frac{9}{12}$. And lastly you choose your third non-yellow marble: $frac{8}{11}$. Now subtract the product from $1$.
    – callculus
    Dec 4 '18 at 18:53










  • I’m confused on how to subtract 1- a fraction 1-10/13*9/12*8/11 do you multiply the numerator and denomination then subtract the 1??
    – J.sant
    Dec 4 '18 at 20:01













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%2f3025759%2fprobability-question-at-least-one-without-replacement%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









1














HINT




  1. Find the probability that none are yellow.

  2. Remember that if $A$ is any event, then $mathbb{P}[A] = 1-mathbb{P}[bar{A}]$


UPDATE




  1. The first time you grab a yellow ball with a chance of 3/13. You want the negation of this, so the chance of that is $1-3/13 = 10/30$.

  2. The second time, you grab a yellow (assuming first time you did not) with a chance 3/12. Third time it will be 3/11.

  3. You want to draw yellow in neither of the tries, the probability of that is $$
    left[1 - frac{3}{13}right]
    times left[1 - frac{3}{12}right]
    times left[1 - frac{3}{11}right]
    = frac{10 cdot 9 cdot 8}{13 cdot 12 cdot 11}
    = frac{60}{143}
    $$


  4. Finally you want the probability that any draw results in a yellow, which is $$1 - frac{60}{143} = frac{83}{143} approx 58%.$$






share|cite|improve this answer























  • This is what I got. 1-(3/13)*(2/12)*(1/11). Is that correct?
    – J.sant
    Dec 4 '18 at 16:35








  • 1




    @J.sant No, you have to calculate $1-P("color{blue}{textrm{No yellow}} textrm{marble is chosen}")$. The probability is approximately $58%$
    – callculus
    Dec 4 '18 at 17:35








  • 1




    So 1-10/13. That’s the probability of none yellow. Is that correct?
    – J.sant
    Dec 4 '18 at 18:22








  • 1




    @J.sant Not really. You chose your first non-yellow marble: $frac{10}{13}$. Then you choose your second non-yellow marble: $frac{9}{12}$. And lastly you choose your third non-yellow marble: $frac{8}{11}$. Now subtract the product from $1$.
    – callculus
    Dec 4 '18 at 18:53










  • I’m confused on how to subtract 1- a fraction 1-10/13*9/12*8/11 do you multiply the numerator and denomination then subtract the 1??
    – J.sant
    Dec 4 '18 at 20:01


















1














HINT




  1. Find the probability that none are yellow.

  2. Remember that if $A$ is any event, then $mathbb{P}[A] = 1-mathbb{P}[bar{A}]$


UPDATE




  1. The first time you grab a yellow ball with a chance of 3/13. You want the negation of this, so the chance of that is $1-3/13 = 10/30$.

  2. The second time, you grab a yellow (assuming first time you did not) with a chance 3/12. Third time it will be 3/11.

  3. You want to draw yellow in neither of the tries, the probability of that is $$
    left[1 - frac{3}{13}right]
    times left[1 - frac{3}{12}right]
    times left[1 - frac{3}{11}right]
    = frac{10 cdot 9 cdot 8}{13 cdot 12 cdot 11}
    = frac{60}{143}
    $$


  4. Finally you want the probability that any draw results in a yellow, which is $$1 - frac{60}{143} = frac{83}{143} approx 58%.$$






share|cite|improve this answer























  • This is what I got. 1-(3/13)*(2/12)*(1/11). Is that correct?
    – J.sant
    Dec 4 '18 at 16:35








  • 1




    @J.sant No, you have to calculate $1-P("color{blue}{textrm{No yellow}} textrm{marble is chosen}")$. The probability is approximately $58%$
    – callculus
    Dec 4 '18 at 17:35








  • 1




    So 1-10/13. That’s the probability of none yellow. Is that correct?
    – J.sant
    Dec 4 '18 at 18:22








  • 1




    @J.sant Not really. You chose your first non-yellow marble: $frac{10}{13}$. Then you choose your second non-yellow marble: $frac{9}{12}$. And lastly you choose your third non-yellow marble: $frac{8}{11}$. Now subtract the product from $1$.
    – callculus
    Dec 4 '18 at 18:53










  • I’m confused on how to subtract 1- a fraction 1-10/13*9/12*8/11 do you multiply the numerator and denomination then subtract the 1??
    – J.sant
    Dec 4 '18 at 20:01
















1












1








1






HINT




  1. Find the probability that none are yellow.

  2. Remember that if $A$ is any event, then $mathbb{P}[A] = 1-mathbb{P}[bar{A}]$


UPDATE




  1. The first time you grab a yellow ball with a chance of 3/13. You want the negation of this, so the chance of that is $1-3/13 = 10/30$.

  2. The second time, you grab a yellow (assuming first time you did not) with a chance 3/12. Third time it will be 3/11.

  3. You want to draw yellow in neither of the tries, the probability of that is $$
    left[1 - frac{3}{13}right]
    times left[1 - frac{3}{12}right]
    times left[1 - frac{3}{11}right]
    = frac{10 cdot 9 cdot 8}{13 cdot 12 cdot 11}
    = frac{60}{143}
    $$


  4. Finally you want the probability that any draw results in a yellow, which is $$1 - frac{60}{143} = frac{83}{143} approx 58%.$$






share|cite|improve this answer














HINT




  1. Find the probability that none are yellow.

  2. Remember that if $A$ is any event, then $mathbb{P}[A] = 1-mathbb{P}[bar{A}]$


UPDATE




  1. The first time you grab a yellow ball with a chance of 3/13. You want the negation of this, so the chance of that is $1-3/13 = 10/30$.

  2. The second time, you grab a yellow (assuming first time you did not) with a chance 3/12. Third time it will be 3/11.

  3. You want to draw yellow in neither of the tries, the probability of that is $$
    left[1 - frac{3}{13}right]
    times left[1 - frac{3}{12}right]
    times left[1 - frac{3}{11}right]
    = frac{10 cdot 9 cdot 8}{13 cdot 12 cdot 11}
    = frac{60}{143}
    $$


  4. Finally you want the probability that any draw results in a yellow, which is $$1 - frac{60}{143} = frac{83}{143} approx 58%.$$







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Dec 4 '18 at 20:25

























answered Dec 4 '18 at 16:15









gt6989b

33.1k22452




33.1k22452












  • This is what I got. 1-(3/13)*(2/12)*(1/11). Is that correct?
    – J.sant
    Dec 4 '18 at 16:35








  • 1




    @J.sant No, you have to calculate $1-P("color{blue}{textrm{No yellow}} textrm{marble is chosen}")$. The probability is approximately $58%$
    – callculus
    Dec 4 '18 at 17:35








  • 1




    So 1-10/13. That’s the probability of none yellow. Is that correct?
    – J.sant
    Dec 4 '18 at 18:22








  • 1




    @J.sant Not really. You chose your first non-yellow marble: $frac{10}{13}$. Then you choose your second non-yellow marble: $frac{9}{12}$. And lastly you choose your third non-yellow marble: $frac{8}{11}$. Now subtract the product from $1$.
    – callculus
    Dec 4 '18 at 18:53










  • I’m confused on how to subtract 1- a fraction 1-10/13*9/12*8/11 do you multiply the numerator and denomination then subtract the 1??
    – J.sant
    Dec 4 '18 at 20:01




















  • This is what I got. 1-(3/13)*(2/12)*(1/11). Is that correct?
    – J.sant
    Dec 4 '18 at 16:35








  • 1




    @J.sant No, you have to calculate $1-P("color{blue}{textrm{No yellow}} textrm{marble is chosen}")$. The probability is approximately $58%$
    – callculus
    Dec 4 '18 at 17:35








  • 1




    So 1-10/13. That’s the probability of none yellow. Is that correct?
    – J.sant
    Dec 4 '18 at 18:22








  • 1




    @J.sant Not really. You chose your first non-yellow marble: $frac{10}{13}$. Then you choose your second non-yellow marble: $frac{9}{12}$. And lastly you choose your third non-yellow marble: $frac{8}{11}$. Now subtract the product from $1$.
    – callculus
    Dec 4 '18 at 18:53










  • I’m confused on how to subtract 1- a fraction 1-10/13*9/12*8/11 do you multiply the numerator and denomination then subtract the 1??
    – J.sant
    Dec 4 '18 at 20:01


















This is what I got. 1-(3/13)*(2/12)*(1/11). Is that correct?
– J.sant
Dec 4 '18 at 16:35






This is what I got. 1-(3/13)*(2/12)*(1/11). Is that correct?
– J.sant
Dec 4 '18 at 16:35






1




1




@J.sant No, you have to calculate $1-P("color{blue}{textrm{No yellow}} textrm{marble is chosen}")$. The probability is approximately $58%$
– callculus
Dec 4 '18 at 17:35






@J.sant No, you have to calculate $1-P("color{blue}{textrm{No yellow}} textrm{marble is chosen}")$. The probability is approximately $58%$
– callculus
Dec 4 '18 at 17:35






1




1




So 1-10/13. That’s the probability of none yellow. Is that correct?
– J.sant
Dec 4 '18 at 18:22






So 1-10/13. That’s the probability of none yellow. Is that correct?
– J.sant
Dec 4 '18 at 18:22






1




1




@J.sant Not really. You chose your first non-yellow marble: $frac{10}{13}$. Then you choose your second non-yellow marble: $frac{9}{12}$. And lastly you choose your third non-yellow marble: $frac{8}{11}$. Now subtract the product from $1$.
– callculus
Dec 4 '18 at 18:53




@J.sant Not really. You chose your first non-yellow marble: $frac{10}{13}$. Then you choose your second non-yellow marble: $frac{9}{12}$. And lastly you choose your third non-yellow marble: $frac{8}{11}$. Now subtract the product from $1$.
– callculus
Dec 4 '18 at 18:53












I’m confused on how to subtract 1- a fraction 1-10/13*9/12*8/11 do you multiply the numerator and denomination then subtract the 1??
– J.sant
Dec 4 '18 at 20:01






I’m confused on how to subtract 1- a fraction 1-10/13*9/12*8/11 do you multiply the numerator and denomination then subtract the 1??
– J.sant
Dec 4 '18 at 20:01




















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.





Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


Please pay close attention to the following guidance:


  • 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.


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%2f3025759%2fprobability-question-at-least-one-without-replacement%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

Berounka

Sphinx de Gizeh

Different font size/position of beamer's navigation symbols template's content depending on regular/plain...