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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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New post 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

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  [#permalink]

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New post 16 Nov 2009, 03:13
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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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Re: Probability: Playing Cards  [#permalink]

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New post 16 Nov 2009, 06:47
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Thank you Ian,
You and Bunuel make math problems sound so simple. Kudos.
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Re: Probability: Playing Cards  [#permalink]

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New post 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WHAT does this statement implies that 10 cards are withdrawn with replacement or without replacement ??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  [#permalink]

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New post 28 Nov 2012, 04:11
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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WHAT does this statement implies that 10 cards are withdrawn with replacement or without replacement ??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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Re: Probability: Playing Cards  [#permalink]

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New post 28 Nov 2012, 08:30
1
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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Re: Probability: Playing Cards  [#permalink]

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New post 29 Nov 2012, 04:51
1
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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New post 22 Sep 2013, 10:52
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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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New post 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  [#permalink]

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New post 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  [#permalink]

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New post 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  [#permalink]

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New post 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  [#permalink]

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New post 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: 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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New post 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.

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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New post 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  [#permalink]

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New post 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!

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

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New post 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.

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Hi 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/if-40-people ... 97015.html
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Re: Laura has a deck of standard playing cards with 13 of the 52 &nbs [#permalink] 22 Apr 2018, 08:49
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