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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] New post 15 Nov 2009, 21:28
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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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Re: Probability: Playing Cards [#permalink] New post 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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Re: Probability: Playing Cards [#permalink] New post 16 Nov 2009, 05:47
Thank you Ian,
You and Bunuel make math problems sound so simple. Kudos.
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Re: Probability: Playing Cards [#permalink] New post 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WHAT does this statement implies that 10 cards are withdrawn with replacement or without replacement ??
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Re: Probability: Playing Cards [#permalink] New post 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WHAT does this statement implies that 10 cards are withdrawn with replacement or without replacement ??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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Re: Probability: Playing Cards [#permalink] New post 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WHAT does this statement implies that 10 cards are withdrawn with replacement or without replacement ??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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Re: Probability: Playing Cards [#permalink] New post 29 Nov 2012, 03:51
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Expert's post
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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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Laura has a deck of standard playing cards with 13 of the 52 [#permalink] New post 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.
Re: Laura has a deck of standard playing cards with 13 of the 52   [#permalink] 22 Sep 2013, 09:52
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