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

It is currently 16 Sep 2014, 05:57

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If the probability of rain on any given day in City X is 50

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 25 Sep 2007
Posts: 22
Followers: 0

Kudos [?]: 6 [0], given: 0

If the probability of rain on any given day in City X is 50 [#permalink] New post 04 Jan 2008, 15:01
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

86% (01:59) correct 14% (00:58) wrong based on 162 sessions
If the probability of rain on any given day in City X is 50 percent, what is the probability that it rains on exactly 3 days in a 5-day period?

(A) 8/125
(B) 2/25
(C) 5/16
(D) 8/25
(E) 3/4
[Reveal] Spoiler: OA
Director
Director
User avatar
Joined: 08 Jun 2007
Posts: 583
Followers: 2

Kudos [?]: 69 [0], given: 0

GMAT Tests User
Re: Probability Question [#permalink] New post 04 Jan 2008, 15:11
JuliaS wrote:
If the probability of rain on any given day in City X is 50 percent, what is the probability that it rains on exactly 3 days in a 5-day period?

(A) 8/125
(B) 2/25
(C) 5/16
(D) 8/25
(E) 3/4

Thanks a lot!


welcome to the forum

total possibilties 2^5 = 32
rain combinations 5c3 = 10
10/32 = 5/16
Director
Director
avatar
Joined: 01 May 2007
Posts: 795
Followers: 1

Kudos [?]: 66 [0], given: 0

GMAT Tests User
Re: Probability Question [#permalink] New post 04 Jan 2008, 16:55
Why is total possibilties 2^5 = 32?
Intern
Intern
avatar
Joined: 30 Dec 2007
Posts: 10
Followers: 0

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

Re: Probability Question [#permalink] New post 04 Jan 2008, 18:19
vscid wrote:
yeah how did u arrive at 2^5.

Let me try to elaborate
Each day, we have 2 possibilities, rain or not rain, therefore the total possibility of 5 days is 2^5=32
Then, we pick 3 rainy days randomly from 5 days, 5C3 = 10
10/32=5/16
3 KUDOS received
Manager
Manager
User avatar
Joined: 22 Jul 2009
Posts: 192
Followers: 4

Kudos [?]: 189 [3] , given: 18

GMAT Tests User
Re: Probability Question [#permalink] New post 18 Sep 2009, 17:45
3
This post received
KUDOS
Binomial distribution formula: C(n,k) * p^k * (1-p)^(n-k)

Given that the probability of Rain happening is p (=1/2) and not happening is 1-p (=1-1/2=1/2),
=> Probability of Rain happening k times (=3) in n repeated tests (=5)
= C(5,3) * (1/2)^3 * (1-1/2)^(5-3)
= C(5,3) * (1/2)^5
= 10/32
= 5/16
_________________

Please kudos if my post helps.

2 KUDOS received
Manager
Manager
avatar
Joined: 27 Oct 2008
Posts: 186
Followers: 1

Kudos [?]: 77 [2] , given: 3

GMAT Tests User
Re: Probability Question [#permalink] New post 27 Sep 2009, 10:02
2
This post received
KUDOS
If the probability of rain on any given day in City X is 50 percent, what is the probability that it rains on exactly 3 days in a 5-day period?

(A) 8/125
(B) 2/25
(C) 5/16
(D) 8/25
(E) 3/4

Soln:
Let Y represent raining on a day and N represent Not raining on a day
So for it to rain 3 out of 5 days we have YYYNN.
Since the order in which it rains in 5 days matters hence we find the total number of possibilities
But since Y has a happened 3 times and N has happened 2 times we cannot distinguish between them and hence divide by the repetitions . Thus we need to divide by (3! * 2!)
=> 5!/(2! * 3!)
=> 10 ways

Now since on each day it can rain or it cannot rain. Thus total outcomes is
=> 2 * 2 * 2 * 2 * 2
=> 32

So probability that it rains on exactly 3 days is
= 10/32
= 5/16

Ans is C
Manager
Manager
avatar
Joined: 03 Aug 2011
Posts: 241
Location: United States
Concentration: General Management, Entrepreneurship
GMAT 1: 750 Q49 V44
GPA: 3.38
WE: Engineering (Computer Software)
Followers: 1

Kudos [?]: 39 [0], given: 12

Re: Probability Question [#permalink] New post 03 Aug 2011, 18:10
Hi,

I'm confused by the answers, only one answer actually has the 50% probability factored in. How come all the other answers just seemed to mention how many ways to choose 3 days in 5 days?

Seems like 50% is a special case, because when you do 5c3, the 3 days could be 3 days of rain or even 3 days of no rain. They all end up being the same probability because of the 50%.

how would this be solved with 20%? 80%?
Manager
Manager
avatar
Joined: 06 Feb 2011
Posts: 84
GMAT 1: Q V
GMAT 2: Q V
GMAT 3: Q V
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 8 [0], given: 11

GMAT Tests User
Re: Probability Question [#permalink] New post 05 Aug 2011, 12:45
pinchharmonic wrote:
Hi,

I'm confused by the answers, only one answer actually has the 50% probability factored in. How come all the other answers just seemed to mention how many ways to choose 3 days in 5 days?

Seems like 50% is a special case, because when you do 5c3, the 3 days could be 3 days of rain or even 3 days of no rain. They all end up being the same probability because of the 50%.

how would this be solved with 20%? 80%?


Eg: For the 20% possibility of rain it will be (1/5)^3 * (4/5)^2* (5C3)
Intern
Intern
avatar
Joined: 01 Dec 2011
Posts: 3
Followers: 0

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

Re: If the probability of rain on any given day in City X is 50 [#permalink] New post 27 Feb 2012, 02:15
Could you tell me why it is a combination and not a permutation?

N = 3C5 x 1/8 x 1/4

why do i have to divide by 2! ?
Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29641
Followers: 3488

Kudos [?]: 26195 [2] , given: 2706

Re: If the probability of rain on any given day in City X is 50 [#permalink] New post 27 Feb 2012, 02:40
2
This post received
KUDOS
Expert's post
flokki wrote:
If the probability of rain on any given day in City X is 50 percent, what is the probability that it rains on exactly 3 days in a 5-day period?

(A) 8/125
(B) 2/25
(C) 5/16
(D) 8/25
(E) 3/4

Could you tell me why it is a combination and not a permutation?

N = 3C5 x 1/8 x 1/4

why do i have to divide by 2! ?


The probability of rain each day is 1/2 and the probability of no rain is also 1/2. C^3_5=10 represent ways to choose on which 3 days out of 5 there will be a rain, so P=C^3_5*(\frac{1}{2})^3*(\frac{1}{2})^2=\frac{10}{32}=\frac{5}{16}.

Answer: C.

Or think about it this way: we want the probability of the following event: RRRNN, where R represent rain day and N represents no-rain day. Now, each R and each N have individual probability of 1/2, so (\frac{1}{2})^5.

But the case of RRRNN can occur in many ways: RRRNN, RRNRRN, RNRRN, NRRRN, ... basically it will be equla to # of arrangements (permutations) of 5 letters RRRNN out of which there are 3 identical R's and 2 identical N's. That # of arrangements is \frac{5!}{3!2!}, (notice that it's the same as C^3_5). So, finally P=\frac{5!}{3!2!}*(\frac{1}{2})^5=\frac{5}{16}.

Answer: C.

For more on this topic check Combinations and Probability chapters of Math Book:
math-combinatorics-87345.html
math-probability-87244.html

Also check similar questions to practice:
if-the-probability-of-rain-on-any-given-day-is-50-what-is-99577.html
on-saturday-morning-malachi-will-begin-a-camping-vacation-100297.html
what-is-the-probability-that-a-field-gun-will-hit-thrice-on-127334.html
there-is-a-90-chance-that-a-registered-voter-in-burghtown-56812.html
combination-ps-55071.html
the-probability-that-a-family-with-6-children-has-exactly-88945.html?

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

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.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 01 Dec 2011
Posts: 3
Followers: 0

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

Re: If the probability of rain on any given day in City X is 50 [#permalink] New post 27 Feb 2012, 02:58
thank you for your answer!

I just started with permutations and probability.

I still dont understand why we use the combination formula and not the permutation one.

Is it because we do not differentiate between one rainy day and the other? are they all the same for us?

Are most Gmat questions at this level?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29641
Followers: 3488

Kudos [?]: 26195 [0], given: 2706

Re: If the probability of rain on any given day in City X is 50 [#permalink] New post 27 Feb 2012, 03:10
Expert's post
flokki wrote:
thank you for your answer!

I just started with permutations and probability.

I still dont understand why we use the combination formula and not the permutation one.

Is it because we do not differentiate between one rainy day and the other? are they all the same for us?

Are most Gmat questions at this level?


Yes, we do not differentiate between RRR and NN: for example RRRNN means that it was raining on the first three days and we have no reason to differentiate between them. Also notice that most GMAT combination/probability questions are fairly straightforward and can be solved in several ways. This problem is also dealing with a simple concept explained in the links I sited above, so I'd recommend to brush your fundamentals on combinations before you move to the problems.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

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.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 24 Feb 2012
Posts: 33
Followers: 0

Kudos [?]: 7 [0], given: 18

Re: If the probability of rain on any given day in City X is 50 [#permalink] New post 29 Feb 2012, 10:26
Binomial formula b(x; n, p) = nCx p^x (1-p)^ n-x
n=3; m=5; p=1/2; 1-p=1/2
b(3; 5, 1/2) = 5C3 * 1/2^2 * 1/2^5
= 10 * 1/32
= 10/32
= 5/16
1 KUDOS received
Manager
Manager
avatar
Joined: 13 Oct 2012
Posts: 78
Concentration: General Management, Leadership
Schools: IE '15 (A)
GMAT 1: 760 Q49 V46
Followers: 1

Kudos [?]: -15 [1] , given: 0

If the probability of rain on any given day in City X is 50 [#permalink] New post 07 Jan 2013, 11:42
1
This post received
KUDOS
select three rainy days out of 5 = 5C3 = 10
probability of 3 rainy and 2 non rainy days = (1/2)^5

Answer = 10 * 1/32 = 5/16
Manager
Manager
avatar
Joined: 18 Oct 2011
Posts: 92
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
Followers: 2

Kudos [?]: 24 [0], given: 0

Re: Probability it with rain on 3 days in a five day ? [#permalink] New post 07 Jan 2013, 14:01
probabiliy of raining on 3 days (1/2)^3 x (1/2)^2 = 1/32

the total number of arragements of rain on 3 days and no rain on 2 days is 5!/2!3! = 10

therefore, probability of raining on exactly 3 days during a 5 day week is 10/32 = 5/16
Re: Probability it with rain on 3 days in a five day ?   [#permalink] 07 Jan 2013, 14:01
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic If the probability of rain on any given day in city x is 50% Alchemist1320 4 12 Jul 2011, 01:23
If the probability of rain on any given day in City X is 50 Vlad77 7 06 Aug 2007, 09:17
The probability of rain in City X is 50% on any given day. gk3.14 6 20 Aug 2006, 12:05
If the probability of rain on any given day in CityX is 50%, pesquadero 3 01 Jun 2006, 19:19
If the probability of rain on any given day in City X is 50 tbetten 6 22 Jun 2005, 15:58
Display posts from previous: Sort by

If the probability of rain on any given day in City X is 50

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.