Laura has a deck of standard playing cards with 13 of the 52 : GMAT Problem Solving (PS)
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# Laura has a deck of standard playing cards with 13 of the 52

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Laura has a deck of standard playing cards with 13 of the 52 [#permalink]

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15 Nov 2009, 21:28
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65% (04:13) correct 35% (01:38) wrong based on 573 sessions

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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 28 Nov 2012, 02:27, edited 1 time in total.
Renamed the topic and edited the question.
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16 Nov 2009, 02:13
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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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16 Nov 2009, 05:47
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Thank you Ian,
You and Bunuel make math problems sound so simple. Kudos.
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27 Nov 2012, 13:05
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WHAT does this statement implies that 10 cards are withdrawn with replacement or without replacement ??
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28 Nov 2012, 03:11
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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WHAT does this statement implies that 10 cards are withdrawn with replacement or without replacement ??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.

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28 Nov 2012, 07:30
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WHAT does this statement implies that 10 cards are withdrawn with replacement or without replacement ??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 X-may 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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29 Nov 2012, 03:51
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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 X-may 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 [#permalink]

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22 Sep 2013, 09:52
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 [#permalink]

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09 Feb 2015, 01:07
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Re: Laura has a deck of standard playing cards with 13 of the 52 [#permalink]

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16 Feb 2016, 07:19
Hello from the GMAT Club BumpBot!

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Re: Laura has a deck of standard playing cards with 13 of the 52 [#permalink]

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09 Apr 2016, 01:36
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 [#permalink]

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19 Apr 2016, 09:10
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 [#permalink]

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25 May 2016, 10:44
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 [#permalink]

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25 Jul 2016, 07:34
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.

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Re: Laura has a deck of standard playing cards with 13 of the 52 [#permalink]

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25 Jul 2016, 07:42
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.

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: laura-has-a-deck-of-standard-playing-cards-with-13-of-the-86902.html#p1148293

Hope it helps.
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Re: Laura has a deck of standard playing cards with 13 of the 52 [#permalink]

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27 Jul 2016, 12:09
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.

check this out , I am 100% sure , explanation will answer your question.

a-certain-team-has-12-members-including-joey-a-three-131321.html#p1078315
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Re: Laura has a deck of standard playing cards with 13 of the 52 [#permalink]

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27 Jul 2016, 12:22
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.

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Re: Laura has a deck of standard playing cards with 13 of the 52   [#permalink] 27 Jul 2016, 12:22
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