Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 29 Apr 2016, 23:25

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# 2 cards are drawn at random

Author Message
TAGS:

### Hide Tags

Manager
Joined: 19 Aug 2010
Posts: 77
Followers: 3

Kudos [?]: 23 [0], given: 2

2 cards are drawn at random [#permalink]

### Show Tags

19 Dec 2010, 10:02
00:00

Difficulty:

(N/A)

Question Stats:

40% (01:43) correct 60% (01:12) wrong based on 7 sessions

### HideShow timer Statictics

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?
Math Expert
Joined: 02 Sep 2009
Posts: 32539
Followers: 5626

Kudos [?]: 68240 [1] , given: 9797

Re: 2 cards are drawn at random [#permalink]

### Show Tags

19 Dec 2010, 10:30
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 9227
Followers: 454

Kudos [?]: 114 [0], given: 0

Re: 2 cards are drawn at random [#permalink]

### Show Tags

19 Dec 2015, 04:48
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
VP
Joined: 08 Jul 2010
Posts: 1184
Location: India
GMAT: INSIGHT
WE: Education (Education)
Followers: 40

Kudos [?]: 927 [0], given: 40

Re: 2 cards are drawn at random [#permalink]

### Show Tags

22 Dec 2015, 02:08
Expert's post
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
Call us : +91-9999687183 / 9891333772

http://www.GMATinsight.com/testimonials.html

Contact for One-on-One LIVE ONLINE (SKYPE Based) or CLASSROOM Quant/Verbal FREE Demo Class

GMATinsight
107, 1st Floor, Krishna Mall,
Sector-12 (Main market),
Dwarka, New Delhi-110075

______________________________________________________
Please press the if you appreciate this post !!

Re: 2 cards are drawn at random   [#permalink] 22 Dec 2015, 02:08
Similar topics Replies Last post
Similar
Topics:
3 If 3 cards are selected at random from the deck of 52 cards then What 1 27 Jul 2015, 06:05
3 If 2 cards are selected (with replacement) at random from the deck of 2 27 Jul 2015, 05:48
If 2 cards are selected at random from the deck of 52 cards then What 1 27 Jul 2015, 05:45
1 If 2 cards are selected at random from the pack of 52 cards then What 1 27 Jul 2015, 05:38
5 Four cards are randomly drawn from a pack of 52 cards. Find 15 02 Jun 2010, 00:36
Display posts from previous: Sort by