NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 09:33 It is currently 25 Apr 2024, 09:33
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Peter took a 52-card deck of cards and removed all small cards

User avatar
gmatprep258
Intern
Intern
Joined: 27 Sep 2015
Posts: 1
Own Kudos [?]: 2 [2]
Given Kudos: 0
Send PM
Peter took a 52-card deck of cards and removed all small cards [#permalink] New post   13 Oct 2015, 11:27
2
Bookmarks
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

100% (00:52) correct 0% (00:00) wrong based on 22 sessions
Hide Show timer Statistics
Peter took a 52-card deck of cards and removed all small cards, all spades, and all clubs.
The only remaining cards were 10, Jack, Queen, King, and Ace in the suits of heart and
diamond. Of these 10 cards, he deals himself 5 cards. What is the probability that Peter
deals himself at least one pair of cards?

A. 7/10
B. 17/33
C. 55/63
D. 66/165
E. 18/25

Note- This is a question from GMATPill exam. I do not have the answer to this question.

Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
avatar
pate13
Manager
Manager
Joined: 02 Sep 2014
Posts: 62
Own Kudos [?]: 243 [0]
Given Kudos: 86
Location: United States
Concentration: Strategy, International Business
Schools: CBS '20 Tuck '20 Booth '20 Sloan '20
GMAT 1: 720 Q48 V41
GMAT 2: 700 Q47 V40
GPA: 3.26
WE:Consulting (Consulting)
Send PM
GMAT ToolKit User Reviews Badge
Re: Peter took a 52-card deck of cards and removed all small cards [#permalink] New post   13 Oct 2015, 12:09
gmatprep258 wrote:
Peter took a 52-card deck of cards and removed all small cards, all spades, and all clubs.
The only remaining cards were 10, Jack, Queen, King, and Ace in the suits of heart and
diamond. Of these 10 cards, he deals himself 5 cards. What is the probability that Peter
deals himself at least one pair of cards?

A. 7/10
B. 17/33
C. 55/63
D. 66/165
E. 18/25

Note- This is a question from GMATPill exam. I do not have the answer to this question.


The only way that he doesn't deal a pair is if he deals 10,J,Q,K,A. So the probability of dealing a pair will be 1 - the probability of dealing 10,J,Q,K,A.

The total number of combinations is \(10*9*8*7*6\), which equals 30240

The number of ways to deal 10,J,Q,K,A or a variance of it is \(10*8*6*4*2\), which equals 3840

1 - 3840/30240 = 26400/30240. That will roughly equal 26/30, which when doubled is 52/60. That is very close to C, which is the answer. We can estimate on this problem because the answer choices are fairly far apart and because the other closest answer has a denominator of 25, which is not a factor of 30240.


C
avatar
bubchucks
Intern
Intern
Joined: 13 Oct 2015
Posts: 1
Own Kudos [?]: [0]
Given Kudos: 6
Send PM
Re: Peter took a 52-card deck of cards and removed all small cards [#permalink] New post   13 Oct 2015, 14:49
gmatprep258 wrote:
Peter took a 52-card deck of cards and removed all small cards, all spades, and all clubs.
The only remaining cards were 10, Jack, Queen, King, and Ace in the suits of heart and
diamond. Of these 10 cards, he deals himself 5 cards. What is the probability that Peter
deals himself at least one pair of cards?

A. 7/10
B. 17/33
C. 55/63
D. 66/165
E. 18/25

Note- This is a question from GMATPill exam. I do not have the answer to this question.

P(at least 1 pair) = 1 - P(no Pairs)
P(no pairs) = number of hands dealt with no pairs / total possible number of hands

Number of hands dealt with no pairs has to be 10 J Q K A but with differing suits of hearts and diamonds. Since there are only two suits to pick from for a hand of 5 cards (just like a Coin Flip problem) total number of hands with no pairs = 2^5 = 32

Total possible number of hands is 10 C 5 = 10*9*8*7*6/ 5*4*3*2*1 = 252

Therefore 1-32/252 = 1- 8/63 = 55/63

Answer C
User avatar
THECEO123
Intern
Intern
Joined: 27 Jun 2015
Posts: 4
Own Kudos [?]: 16 [1]
Given Kudos: 0
Concentration: Marketing, Entrepreneurship
Schools: Haas '18
Send PM
Re: Peter took a 52-card deck of cards and removed all small cards [#permalink] New post   13 Oct 2015, 19:26
1
Kudos
gmatprep258 wrote:
Peter took a 52-card deck of cards and removed all small cards, all spades, and all clubs.
The only remaining cards were 10, Jack, Queen, King, and Ace in the suits of heart and
diamond. Of these 10 cards, he deals himself 5 cards. What is the probability that Peter
deals himself at least one pair of cards?

A. 7/10
B. 17/33
C. 55/63
D. 66/165
E. 18/25

Note- This is a question from GMATPill exam. I do not have the answer to this question.


Total number of ways the 10 cards can be arranged in groups of 5
= (10 x 9 x 8 x 7 x 6) / (5 x 4 x 3 x 2 x 1)
= 252

Therefore all probabilities will be a factor of 252: that is 0/252 to 252/252

Check answer choices to see which denominator is a factor of 252
A. 7/10 -> 252/10 - leaves remainder - wrong
B. 17/33 -> 252/33 - leaves remainder - wrong
C. 55/63 -> 252/63 - remainder = 0; possible choice
D. 66/165 -> 252/165 - leaves remainder - wrong
E. 18/25 -> 252/25 - leaves remainder - wrong

Of all the choices c is the correct option. No need to continue!

Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
GMAT Club Bot
gmatclubot
Re: Peter took a 52-card deck of cards and removed all small cards [#permalink]
13 Oct 2015, 19:26
Moderators:
Bunuel
Math Expert
92914 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions