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Laura has a deck of standard playing cards with 13 of the 52
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Updated on: 28 Nov 2012, 03:27
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Laura has a deck of standard playing cards with 13 of the 52 cards designated as a "heart." If Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart? (A) 1/4 (B) 1/5 (C) 5/26 (D) 12/42 (E) 13/42
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Originally posted by ctrlaltdel on 15 Nov 2009, 22:28.
Last edited by Bunuel on 28 Nov 2012, 03:27, edited 1 time in total.
Renamed the topic and edited the question.




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Re: Probability: Playing Cards
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16 Nov 2009, 03:13
Every card has a 13/52 = 1/4 chance of being a heart; it doesn't matter if it's the top card in the deck or the tenth card in the deck.
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Re: Probability: Playing Cards
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16 Nov 2009, 06:47
Thank you Ian, You and Bunuel make math problems sound so simple. Kudos.



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Re: Probability: Playing Cards
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27 Nov 2012, 14:05
and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart?
WHAT does this statement implies that 10 cards are withdrawn with replacement or without replacement ??



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Re: Probability: Playing Cards
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28 Nov 2012, 04:11
himanshuhpr wrote: and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart?
WHAT does this statement implies that 10 cards are withdrawn with replacement or without replacement ?? No replacement there, 10 cards are dealt and we are asked to find the probability that 10th card is a heart. Similar questions to practice: acertainteamhas12membersincludingjoeyathree131321.htmlacertaintelevisionshowhas15sponsorsincludingcompany127423.htmlamedicalresearchermustchooseoneof14patientsto127396.htmlacertainclassconsistsof8studentsincludingkim127730.htmlacertainclubhas10membersincludingharryoneofthe134891.html
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Re: Probability: Playing Cards
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28 Nov 2012, 08:30
Bunuel wrote: himanshuhpr wrote: and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart?
WHAT does this statement implies that 10 cards are withdrawn with replacement or without replacement ?? No replacement there, 10 cards are dealt and we are asked to find the probability that 10th card is a heart. If there is no replacement then how is the (P) that the 10th card is 13/52 ?? there are many cases here to be considered here if there is no replacement such as: H Denotes heart Xmay be any diamond, spade or club. 1. HXXXXXXXXH 2. HHXXXXXXXH 3. HHHXXXXXXH . . . . . 9. HHHHHHHHHH 10. XXXXXXXXXH All cases from 1 to 10 will have different probabilities for heart to be at the 10th place and it will take hell lot of time to calculate all of them. For according to me the above solution by Ian is only valid if cards are replaced (Every card has a 13/52 = 1/4 chance of being a heart; it doesn't matter if it's the top card in the deck or the tenth card in the deck.)If that's the case that brings back me to my original question  how do we determine that the cards are replaced or not ?? based on the question given ....



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Re: Probability: Playing Cards
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29 Nov 2012, 04:51
himanshuhpr wrote: Bunuel wrote: himanshuhpr wrote: and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart?
WHAT does this statement implies that 10 cards are withdrawn with replacement or without replacement ?? No replacement there, 10 cards are dealt and we are asked to find the probability that 10th card is a heart. If there is no replacement then how is the (P) that the 10th card is 13/52 ?? there are many cases here to be considered here if there is no replacement such as: H Denotes heart Xmay be any diamond, spade or club. 1. HXXXXXXXXH 2. HHXXXXXXXH 3. HHHXXXXXXH . . . . . 9. HHHHHHHHHH 10. XXXXXXXXXH All cases from 1 to 10 will have different probabilities for heart to be at the 10th place and it will take hell lot of time to calculate all of them. For according to me the above solution by Ian is only valid if cards are replaced (Every card has a 13/52 = 1/4 chance of being a heart; it doesn't matter if it's the top card in the deck or the tenth card in the deck.)If that's the case that brings back me to my original question  how do we determine that the cards are replaced or not ?? based on the question given .... When we have a case with replacement it's always clearly mentioned in the question. We are told that "Laura deals 10 cards off the top of the deck", which means that there is no replacement whatsoever. As for the question, concept behind it is discussed in the topics given in my previous post.
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Re: Laura has a deck of standard playing cards with 13 of the 52
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22 Sep 2013, 10:52
ctrlaltdel wrote: Laura has a deck of standard playing cards with 13 of the 52 cards designated as a "heart." If Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart? Hi! I went through all the similar problems provided by Bunuel and was able to understand and solve them. However, I am still not able to get why this is not an arrangement problem. Why do we need to ignore the number 10? Bunuel/Karishma, kindly elaborate. I solved the question using reverse probability: 1 P(10th is not heart) = 1 (3*13)/52 = 1/4.



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Re: Laura has a deck of standard playing cards with 13 of the 52
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09 Apr 2016, 02:36
ctrlaltdel wrote: Laura has a deck of standard playing cards with 13 of the 52 cards designated as a "heart." If Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart?
(A) 1/4 (B) 1/5 (C) 5/26 (D) 12/42 (E) 13/42 So this one has a lot of language to confuse. question only talks about the 10th card being heart. so probability for this card being heart is 13/52 = 1/4 only.
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Re: Laura has a deck of standard playing cards with 13 of the 52
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19 Apr 2016, 10:10
IanStewart wrote: Every card has a 13/52 = 1/4 chance of being a heart; it doesn't matter if it's the top card in the deck or the tenth card in the deck. I chose this answer because the alternate method seemed too long for GMAT. But I am just confused that what if the first 9 cards dealt are hearts  then the probability that the 10th card is hearts will be reduced.! I know you've mentioned that it does not matter if it is the 1st card or the 10th card but could you please elaborate on this? Thank you!!!



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Re: Laura has a deck of standard playing cards with 13 of the 52
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25 May 2016, 11:44
How would the problem change if the 14th Card to be dealt would have been a heart instead of 10th?



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Laura has a deck of standard playing cards with 13 of the 52
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25 Jul 2016, 08:34
Hello,
I believe this question has something to do with whether the previous cards were seen. If the cards were not seen, then the probability of 1/4 makes sense else the question will be a bit weird to answer.
Please comment.



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Re: Laura has a deck of standard playing cards with 13 of the 52
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25 Jul 2016, 08:42
AkashKashyap wrote: Hello,
I believe this question has something to do with whether the previous cards were seen. If the cards were not seen, then the probability of 1/4 makes sense else the question will be a bit weird to answer.
Please comment. It does not matter whether Laura knows the results, the point is that we don't know the results, hence the answer of 1/4. Please check similar questions here: laurahasadeckofstandardplayingcardswith13ofthe86902.html#p1148293Hope it helps.
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Re: Laura has a deck of standard playing cards with 13 of the 52
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27 Jul 2016, 13:09
AkashKashyap wrote: Hello,
I believe this question has something to do with whether the previous cards were seen. If the cards were not seen, then the probability of 1/4 makes sense else the question will be a bit weird to answer.
Please comment. check this out , I am 100% sure , explanation will answer your question. acertainteamhas12membersincludingjoeyathree131321.html#p1078315



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Re: Laura has a deck of standard playing cards with 13 of the 52
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27 Jul 2016, 13:22
ctrlaltdel wrote: Laura has a deck of standard playing cards with 13 of the 52 cards designated as a "heart." If Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart?
(A) 1/4 (B) 1/5 (C) 5/26 (D) 12/42 (E) 13/42 Desired outcomes= 13 Total outcomes= 52 Probability of getting any card as the heart card= 13/52= 1/4 And the same probability will be for 10th card as well. A is the answer
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Re: Laura has a deck of standard playing cards with 13 of the 52
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18 Feb 2018, 23:07
I was confused as well,but the solution is something like this. Let's assume the question is to find the probability of drawing second card as heart instead of 10th? How we will approach this problem is: A) find the probability that first drawn Is heart and second drawn is heart too i.e. (13/52*12/51) B) find the probability that first drawn is not a heart and second drawn is a heart(39/52*13/51) Adding the two will give you 1/4. The above example is to give a sense of what is happening in this question. Since we don't know the outcome we can't assume weather the first draw is a heart or not a heart. We added the outcome of two situations. I see a lot of people saying how can the probability of drawing 10th card as a heart be 1/4 when all the cards from 1 to 9 can be heart. Yes! Certainly it can be but its one of the cases. Adding all such cases will give you 1/4. And had we known the result of previous outcomes, indeed the question would be different. As Bunuel said. May be laura knows the outcome but we don't. Great question. Thanks guys! Regards M Posted from my mobile devicePosted from my mobile device



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Re: Laura has a deck of standard playing cards with 13 of the 52
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22 Apr 2018, 08:49
Bunuel wrote: himanshuhpr wrote: and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart?
WHAT does this statement implies that 10 cards are withdrawn with replacement or without replacement ?? No replacement there, 10 cards are dealt and we are asked to find the probability that 10th card is a heart. Similar questions to practice: http://gmatclub.com/forum/acertaintea ... 31321.htmlhttp://gmatclub.com/forum/acertaintel ... 27423.htmlhttp://gmatclub.com/forum/amedicalres ... 27396.htmlhttp://gmatclub.com/forum/acertaincla ... 27730.htmlhttp://gmatclub.com/forum/acertainclu ... 34891.htmlHi Bunuel, I was looking a similar problem where you solved by an approach, which I am applying here i am not getting the solution. Can you please help me with this? 1*9c51/10c52 Problem i am referring to : https://gmatclub.com/forum/if40people ... 97015.html



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Re: Laura has a deck of standard playing cards with 13 of the 52
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18 Jan 2019, 21:00
Bunuel wrote: himanshuhpr wrote: Bunuel wrote: and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart?
WHAT does this statement implies that 10 cards are withdrawn with replacement or without replacement ?? No replacement there, 10 cards are dealt and we are asked to find the probability that 10th card is a heart. If there is no replacement then how is the (P) that the 10th card is 13/52 ?? there are many cases here to be considered here if there is no replacement such as: H Denotes heart Xmay be any diamond, spade or club. 1. HXXXXXXXXH 2. HHXXXXXXXH 3. HHHXXXXXXH . . Hello bunuel can you please provide the link to your previous post where you have discussed the concept Posted from my mobile device



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Re: Laura has a deck of standard playing cards with 13 of the 52
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24 Jan 2019, 06:56
I think a slightly different solution may involve the expected value.Since before Laura picks any card the probability of picking a heart is 1/4,after 9 cards the expected value of picking a heart is 9/4=2,25 which means that after 9 cards Laura has statistically picked 6,75 non hearts and 2,25 hearts. Now you have 10,75 hearts left out of 43 cards(529) so the probability is now 10,75/43>1075/4300> 1/4.



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Re: Laura has a deck of standard playing cards with 13 of the 52
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07 May 2019, 08:42
For anyone looking at this problem and thinking "I need to consider what the first 9 cards are", perhaps I can offer an easy explanation of why that's unnecessary (if you did not think that, there's no reason to read any further!). In a deck of cards, we have 13 hearts, 13 spades, 13 clubs and 13 diamonds, out of 52 cards, so 1/4 of the deck is hearts. Consider these questions: If a magician spreads out a deck of cards, and asks you to choose one at random, what's the probability you pick a heart? It's 13/52 = 1/4, since you're just picking one card at random. Now if the magician fans the deck of cards, and asks you to choose one, and you happen to pick the 10th card, what is the probability you picked a heart? Again, it's 1/4, for the same reason as before; you're still picking a random card from the deck. Whether you pick the 1st card, the 10th card, the 37th card or the last card, each has a 1/4 probability of being a heart. But that's the same question as the one in the OP above  Laura is just picking the tenth card from the deck. Unless you have some information about the top nine cards, the tenth card is just as random as the first one.
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Re: Laura has a deck of standard playing cards with 13 of the 52
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