GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Jul 2018, 06:54

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.

Close

Request Expert Reply

Confirm Cancel

2 cards are drawn at random

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Manager
Manager
User avatar
Joined: 19 Aug 2010
Posts: 69
2 cards are drawn at random [#permalink]

Show Tags

New post 19 Dec 2010, 10:02
1
4
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

56% (01:14) correct 44% (01:29) wrong based on 22 sessions

HideShow timer Statistics

Two cards are drawn at random from a pack of 52 cards. What is the probability that either both are black or both are queens?

Is there a way to solve it without using the combinations formula?
Most Helpful Expert Reply
Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47110
Re: 2 cards are drawn at random [#permalink]

Show Tags

New post 19 Dec 2010, 10:30
2
4
medanova wrote:
Two cards are drawn at random from a pack of 52 cards. What is the probability that either both are black or both are queens?

Is there a way to solve it without using the combinations formula?


Yes, there is.

OR probability:
If Events A and B are independent, the probability that either Event A OR Event B occurs is: \(P(A \ or \ B) = P(A) + P(B) - P(A \ and \ B)\).

This is basically the same as 2 overlapping sets formula:
{total # of items in groups A or B} = {# of items in group A} + {# of items in group B} - {# of items in A and B}.

Note that if event are mutually exclusive then \(P(A \ and \ B)=0\) and the formula simplifies to: \(P(A \ or \ B) = P(A) + P(B)\).

Also note that when we say "A or B occurs" we include three possibilities:
A occurs and B does not occur;
B occurs and A does not occur;
Both A and B occur.

AND probability:
When two events are independent, the probability of both occurring is the product of the probabilities of the individual events: \(P(A \ and \ B) = P(A)*P(B)\).

This is basically the same as Principle of Multiplication: if one event can occur in \(m\) ways and a second can occur independently of the first in \(n\) ways, then the two events can occur in \(mn\) ways.

Back to the original question:
Two cards are drawn at random from a pack of 52 cards. What is the probability that either both are black or both are queens?

\(P(BB \ or QQ)=P(BB)+P(QQ)-P(BQ \ and \ BQ)=\frac{26}{52}*\frac{25}{51}+\frac{4}{52}*\frac{3}{51}-\frac{2}{52}*\frac{1}{51}\) (note \(P(BQ \ and \ BQ)\) means the probability that first card is black queen and the second card is also black queen).

Hope its clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
Expert Post
SVP
SVP
User avatar
P
Joined: 08 Jul 2010
Posts: 2120
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: 2 cards are drawn at random [#permalink]

Show Tags

New post 22 Dec 2015, 02:08
medanova wrote:
Two cards are drawn at random from a pack of 52 cards. What is the probability that either both are black or both are queens?

Is there a way to solve it without using the combinations formula?


Probability that both are black = 26/52*25/51
Probability that both are Queens = 4/52*3/51
Case that is counted in both cases calculated above = (2/52)*(1/51)

Final Probability = (26*25+4*3-2*1)/(52*51)
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

1 KUDOS received
Senior Manager
Senior Manager
User avatar
P
Joined: 29 Jun 2017
Posts: 497
GPA: 4
WE: Engineering (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
Re: 2 cards are drawn at random [#permalink]

Show Tags

New post 23 Aug 2017, 22:29
1
See the solution.
refer to pic attached for the solution
Attachments

IMG_1320.JPG
IMG_1320.JPG [ 1.05 MiB | Viewed 8719 times ]


_________________

Give Kudos for correct answer and/or if you like the solution.

Intern
Intern
avatar
Joined: 18 May 2018
Posts: 8
Re: 2 cards are drawn at random [#permalink]

Show Tags

New post 23 Jun 2018, 01:03
How is it 2C2, can you please explain this?
Re: 2 cards are drawn at random   [#permalink] 23 Jun 2018, 01:03
Display posts from previous: Sort by

2 cards are drawn at random

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.