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

 It is currently 16 Nov 2018, 08:06

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 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

Author Message
TAGS:

Hide Tags

Math Expert
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

18 Jul 2017, 20:19
00:00

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

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

Show Tags

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
Joined: 26 Feb 2016
Posts: 3307
Location: India
GPA: 3.12
The probability of rain on each of five days is 1/6, except on the fir  [#permalink]

Show Tags

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
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

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

Show Tags

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

_________________

If you want to appreciate, just click on Kudos.

Intern
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

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
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

 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®.