February 21, 2019 February 21, 2019 10:00 PM PST 11:00 PM PST Kick off your 2019 GMAT prep with a free 7day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th. February 23, 2019 February 23, 2019 07:00 AM PST 09:00 AM PST Learn reading strategies that can help even nonvoracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 25 Sep 2007
Posts: 20

If the probability of rain on any given day in City X is 50 percent
[#permalink]
Show Tags
Updated on: 05 Feb 2019, 04:08
Question Stats:
79% (01:31) correct 21% (01:54) wrong based on 323 sessions
HideShow timer Statistics
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 5day period? (A) 8/125 (B) 2/25 (C) 5/16 (D) 8/25 (E) 3/4
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by JuliaS on 04 Jan 2008, 15:01.
Last edited by Bunuel on 05 Feb 2019, 04:08, edited 1 time in total.
Renamed the topic and edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 53063

Re: If the probability of rain on any given day in City X is 50 percent
[#permalink]
Show Tags
27 Feb 2012, 02:40
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 5day 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 norain 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: mathcombinatorics87345.htmlmathprobability87244.htmlAlso check similar questions to practice: iftheprobabilityofrainonanygivendayis50whatis99577.htmlonsaturdaymorningmalachiwillbeginacampingvacation100297.htmlwhatistheprobabilitythatafieldgunwillhitthriceon127334.htmlthereisa90chancethataregisteredvoterinburghtown56812.htmlcombinationps55071.htmltheprobabilitythatafamilywith6childrenhasexactly88945.html? Hope it helps.
_________________
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? Extrahard Quant Tests with Brilliant Analytics




Manager
Joined: 27 Oct 2008
Posts: 175

Re: If the probability of rain on any given day in City X is 50 percent
[#permalink]
Show Tags
27 Sep 2009, 10:02
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 5day 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




Director
Joined: 08 Jun 2007
Posts: 545

Re: If the probability of rain on any given day in City X is 50 percent
[#permalink]
Show Tags
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 5day 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
Joined: 01 May 2007
Posts: 770

Re: If the probability of rain on any given day in City X is 50 percent
[#permalink]
Show Tags
04 Jan 2008, 16:55
Why is total possibilties 2^5 = 32?



Intern
Joined: 30 Dec 2007
Posts: 10

Re: If the probability of rain on any given day in City X is 50 percent
[#permalink]
Show Tags
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



Manager
Joined: 22 Jul 2009
Posts: 168

Re: If the probability of rain on any given day in City X is 50 percent
[#permalink]
Show Tags
18 Sep 2009, 17:45
Binomial distribution formula: C(n,k) * p^k * (1p)^(nk) Given that the probability of Rain happening is p (=1/2) and not happening is 1p (=11/2=1/2), => Probability of Rain happening k times (=3) in n repeated tests (=5) = C(5,3) * (1/2)^3 * (11/2)^(53) = C(5,3) * (1/2)^5 = 10/32 = 5/16
_________________
Please kudos if my post helps.



Manager
Joined: 03 Aug 2011
Posts: 214
Location: United States
Concentration: General Management, Entrepreneurship
GPA: 3.38
WE: Engineering (Computer Software)

Re: If the probability of rain on any given day in City X is 50 percent
[#permalink]
Show Tags
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
Joined: 06 Feb 2011
Posts: 59
WE: Information Technology (Computer Software)

Re: If the probability of rain on any given day in City X is 50 percent
[#permalink]
Show Tags
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
Joined: 01 Dec 2011
Posts: 2

Re: If the probability of rain on any given day in City X is 50 percent
[#permalink]
Show Tags
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! ?



Intern
Joined: 01 Dec 2011
Posts: 2

Re: If the probability of rain on any given day in City X is 50 percent
[#permalink]
Show Tags
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?



Math Expert
Joined: 02 Sep 2009
Posts: 53063

Re: If the probability of rain on any given day in City X is 50 percent
[#permalink]
Show Tags
27 Feb 2012, 03:10
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 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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 24 Feb 2012
Posts: 31

Re: If the probability of rain on any given day in City X is 50 percent
[#permalink]
Show Tags
29 Feb 2012, 10:26
Binomial formula b(x; n, p) = nCx p^x (1p)^ nx n=3; m=5; p=1/2; 1p=1/2 b(3; 5, 1/2) = 5C3 * 1/2^2 * 1/2^5 = 10 * 1/32 = 10/32 = 5/16



Intern
Joined: 13 Oct 2012
Posts: 46
Concentration: General Management, Leadership

Re: If the probability of rain on any given day in City X is 50 percent
[#permalink]
Show Tags
07 Jan 2013, 11:42
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
Joined: 18 Oct 2011
Posts: 86
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01302013
GPA: 3.3

Re: If the probability of rain on any given day in City X is 50 percent
[#permalink]
Show Tags
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



Intern
Joined: 14 Jan 2018
Posts: 1

Re: If the probability of rain on any given day in City X is 50 percent
[#permalink]
Show Tags
12 Feb 2018, 12:37
how can we solve this kind of problem with different percentages of probability?
So instead of 50 percent lets say 30 percent, I know how to solve this in the "Binomial formula" way, but what about the "n/N" way (N=total possibilities n=rain combinations) what are the total possibilities in the case of 30 percent chances of rain?
thank you




Re: If the probability of rain on any given day in City X is 50 percent
[#permalink]
12 Feb 2018, 12:37






