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

It is currently 16 Nov 2018, 08:06

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
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • Free GMAT Strategy Webinar

     November 17, 2018

     November 17, 2018

     07:00 AM PST

     09:00 AM PST

    Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
  • GMATbuster's Weekly GMAT Quant Quiz # 9

     November 17, 2018

     November 17, 2018

     09:00 AM PST

     11:00 AM PST

    Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.

The probability of rain on each of five days is 1/6, except on the fir

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50619
The probability of rain on each of five days is 1/6, except on the fir  [#permalink]

Show Tags

New post 18 Jul 2017, 20:19
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

78% (02:15) correct 22% (02:10) wrong based on 115 sessions

HideShow timer Statistics

The probability of rain on each of five days is 1/6, except on the first day, when it is 2/5, and on the last day, when it is 4/5. What is the probability that rain will occur on at least one of the five days?

(A) 1/675
(B) 5/72
(C) 5/27
(D) 22/27
(E) 67/72

_________________

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

Director
Director
User avatar
P
Joined: 18 Aug 2016
Posts: 625
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
GMAT ToolKit User Premium Member Reviews Badge
Re: The probability of rain on each of five days is 1/6, except on the fir  [#permalink]

Show Tags

New post 18 Jul 2017, 20:25
2
Bunuel wrote:
The probability of rain on each of five days is 1/6, except on the first day, when it is 2/5, and on the last day, when it is 4/5. What is the probability that rain will occur on at least one of the five days?

(A) 1/675
(B) 5/72
(C) 5/27
(D) 22/27
(E) 67/72


No rain on all days
\(3/5*5/6*5/6*5/6*1/5 = 15/216\)

Atleast 1 day rain = \(1-15/216 = 201/216 = 67/72\)
_________________

We must try to achieve the best within us


Thanks
Luckisnoexcuse

Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3307
Location: India
GPA: 3.12
Premium Member CAT Tests
The probability of rain on each of five days is 1/6, except on the fir  [#permalink]

Show Tags

New post 18 Jul 2017, 20:29
1
Given data :
Probability of raining on 1st day = \(\frac{2}{5}\)
Probability of raining on other days = \(\frac{1}{6}\)
Probability of raining on 5th day = \(\frac{4}{5}\)

From this we can find probability it didn't rain on
Day 1 = 1 - \(\frac{2}{5}\) = \(\frac{3}{5}\)
Day 2,3,4 = 1 - \(\frac{1}{6}\) = \(\frac{5}{6}\)
Day 5 = 1 - \(\frac{4}{5}\) = \(\frac{1}{5}\)

Since we have been asked to find the probability of rain on at least 1 days,
the easiest was is to find the probability that it doesn't rain on either of the days.

P(Raining on at least one day) = 1 - P(Not raining on single day)
= 1 - (\(\frac{3}{5}*\frac{5}{6}*\frac{5}{6}*\frac{5}{6}*\frac{1}{5}\)) = 1 - \(\frac{5}{72} = \frac{67}{72}\)(Option E)
_________________

You've got what it takes, but it will take everything you've got

Senior Manager
Senior Manager
User avatar
B
Joined: 28 Jun 2015
Posts: 293
Concentration: Finance
GPA: 3.5
Re: The probability of rain on each of five days is 1/6, except on the fir  [#permalink]

Show Tags

New post 18 Jul 2017, 20:55
Bunuel wrote:
The probability of rain on each of five days is 1/6, except on the first day, when it is 2/5, and on the last day, when it is 4/5. What is the probability that rain will occur on at least one of the five days?

(A) 1/675
(B) 5/72
(C) 5/27
(D) 22/27
(E) 67/72


Probability of rain on at least one of the days = 1 - (Probability of rain on no day).

Probability of rain on Day-1 = \(\frac{2}{5}\), no rain = \(\frac{3}{5}\).
Probability of rain on Day-2 = Day-3 = Day-4 = \(\frac{1}{6}\), no rain = \(\frac{5}{6}\).
Probability of rain on Day-4 = \(\frac{4}{5}\), no rain = \(\frac{1}{5}\).

Probability of rain on at least one of the days = \(1 - (\frac{3}{5} * (\frac{5}{6})^{3} * \frac{1}{5}) = 1 - \frac{15}{216} = 1 - \frac{5}{72} = \frac{67}{72}\). Ans - E.
_________________

I used to think the brain was the most important organ. Then I thought, look what’s telling me that.

Intern
Intern
avatar
S
Joined: 19 Dec 2016
Posts: 49
Location: India
Concentration: Technology, Leadership
WE: Consulting (Computer Software)
Re: The probability of rain on each of five days is 1/6, except on the fir  [#permalink]

Show Tags

New post 18 Jul 2017, 21:31
Probability that rain will not happen on any day is-

=(1-2/5)(1-1/6)(1-1/6)(1-1/6)(1-4/5)
=3/5*5/6*5/6*5/6*1/5
=5/72

now for probability of rain to occur on at least one of five days, We will subtract probability of not occurring into 1 i.e

=1-5/72
=67/72

Answer is E
_________________

If you want to appreciate, just click on Kudos.

Intern
Intern
avatar
Joined: 28 Aug 2017
Posts: 1
Re: The probability of rain on each of five days is 1/6, except on the fir  [#permalink]

Show Tags

New post 13 Oct 2017, 22:08
What if it was asked to find the probability of raining for atleast 2 days??

Sent from my Redmi Note 4 using GMAT Club Forum mobile app
GMAT Club Bot
Re: The probability of rain on each of five days is 1/6, except on the fir &nbs [#permalink] 13 Oct 2017, 22:08
Display posts from previous: Sort by

The probability of rain on each of five days is 1/6, except on the fir

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


Copyright

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®.