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

It is currently 20 Oct 2019, 22:14

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

In Rwanda, the chance for rain on any given day is 1/2. What

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

Hide Tags

Find Similar Topics 
Senior Manager
Senior Manager
avatar
Joined: 19 Nov 2004
Posts: 418
Location: SF Bay Area, USA
In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

Show Tags

New post Updated on: 11 Jun 2015, 02:19
2
27
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

73% (01:58) correct 27% (02:04) wrong based on 506 sessions

HideShow timer Statistics

In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 4 out of 7 consecutive days in Rwanda?

A. 4/7
B. 3/7
C. 35/128
D. 4/28
E. 28/135

Originally posted by nocilis on 28 Feb 2005, 15:14.
Last edited by Bunuel on 11 Jun 2015, 02:19, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58443
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

Show Tags

New post 11 Jun 2015, 02:26
4
14
nocilis wrote:
In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 4 out of 7 consecutive days in Rwanda?

A. 4/7
B. 3/7
C. 35/128
D. 4/28
E. 28/135


Similar questions to practice:
if-the-probability-of-rain-on-any-given-day-in-chicago-during-the-summ-187742.html (OG13)
if-the-probability-of-rain-on-any-given-day-is-50-what-is-99577.html
if-the-probability-of-rain-on-any-given-day-in-city-x-is-57957.html
the-chance-of-rain-on-any-given-day-in-tel-aviv-is-50-what-142332.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
a-store-buys-10-bottles-of-alcohol-including-7-bottles-of-55071.html
the-probability-that-a-family-with-6-children-has-exactly-88945.html
if-a-certain-coin-is-flipped-the-probability-that-the-coin-58357.html
what-is-the-probability-that-a-field-gun-will-hit-thrice-on-127334.html
a-store-buys-10-bottles-of-alcohol-including-7-bottles-of-55071.html
the-probability-that-a-family-with-6-children-has-exactly-88945.html
a-gumball-machine-contains-7-blue-5-green-and-4-red-141079.html
a-basket-contains-3-blue-3-red-and-3-yellow-marbles-if-55673.html
there-are-10-solid-colored-balls-in-a-box-including-1-green-135103.html
when-a-random-experiment-is-conducted-the-probability-that-89835.html
if-the-probability-of-sita-getting-selected-to-a-school-is-130643.html
in-a-multiple-choice-test-comprising-5-questions-each-with-136936.html
if-a-certain-coin-is-flipped-the-probability-that-the-coin-58357.html
for-each-player-s-turn-in-a-certain-board-game-a-card-is-141790.html
_________________
General Discussion
Manager
Manager
avatar
Joined: 24 Jan 2005
Posts: 192
Location: Boston
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

Show Tags

New post 28 Feb 2005, 15:20
1
3
The P will be C(7,4)* (1/2^7)

= 35/128

We have to select 4 rainy days from 7 total possible days and then multiply with the probability of each such selection.
Manager
Manager
avatar
Joined: 27 Jan 2005
Posts: 88
Location: San Jose,USA- India
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

Show Tags

New post 28 Feb 2005, 17:34
How would you solve it if the percentage of rain likely on any days is 30% as against the given 50%( or 1/2).
Senior Manager
Senior Manager
avatar
Joined: 19 Nov 2004
Posts: 418
Location: SF Bay Area, USA
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

Show Tags

New post 28 Feb 2005, 18:36
1
Yes, You guys are right.

To add a twist to the problem:

a) What is the probablility that it would rain on 4 consequitive days out of the 7 consequtive days?

b) What is the probablility that it would rain on only 3 alternate days out of the 7 consequtive days?

c) If it rains on the day before, the probability of it raining the next day becomes 1/4. What is the probability that it rains on 4 days out of 7 consecutive days in Rwanda?
VP
VP
User avatar
Joined: 25 Nov 2004
Posts: 1205
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

Show Tags

New post 28 Feb 2005, 19:59
700Plus wrote:
How would you solve it if the percentage of rain likely on any days is 30% as against the given 50%( or 1/2).

Assuming your addition is a contineuation of the original question.
=7C4 * (3/10)^7 =(35x2187)/10^7
VP
VP
User avatar
Joined: 25 Nov 2004
Posts: 1205
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

Show Tags

New post 28 Feb 2005, 20:14
nocilis wrote:
c) If it rains on the day before, the probability of it raining the next day becomes 1/4. What is the probability that it rains on 4 days out of 7 consecutive days in Rwanda?


=7C4 (1/2) (1/2*1/4) (1/2*1/4*1/4) (1/2*1/4*1/4*1/4)
=7C4 (1/2) (1/8) (1/32) (1/128)
=7C4 (1/2) (1/2)^3 (1/2)^5 (1/2)^7
=7C4 (1/2)^16

guys, pls do correct if any.
Manager
Manager
avatar
Joined: 08 Oct 2004
Posts: 120
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

Show Tags

New post 28 Feb 2005, 20:57
3
1
General rule

x successes out of n trials :

P(x)=n!/x!*(n-x)!*(p)^x*(1-p)^n-x

Some stuff from my Stats. class :wink:

P.S. BTW this my first post :wink:
Senior Manager
Senior Manager
User avatar
Joined: 21 Sep 2004
Posts: 453
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

Show Tags

New post 01 Mar 2005, 07:49
1
using Binomial. theorem
nCr (p)^r (q)^n-r

7C4 (1/2)^4 (1/2)^r

which is 35/128
Manager
Manager
avatar
Joined: 28 Oct 2004
Posts: 77
Location: Irvine, CA
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

Show Tags

New post 01 Mar 2005, 10:35
can anyone please tell me why do we have to divide by seven?

My reasoning goest till we multiply for 1/2

I mean, it is a 7C4*1/2, but why divided by seven again?

thanks! :oops: :oops:
_________________
discipline is what I need.
SVP
SVP
User avatar
Joined: 03 Jan 2005
Posts: 1702
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

Show Tags

New post 01 Mar 2005, 11:30
1
OMG this is becoming such a good thought stimulating thread. I like the way you guys are thinking outside of the given question in order to test if you have really grasped the concept and mastered the approach. :good

Kevinw, it was not devided by seven. a^b means a to the power of b. In other words, for the original question people has multiplied C(7,4) by the probabilities of rain for four days and no rain for three days: (1/2)^4*(1/2)^3.
Manager
Manager
avatar
Joined: 01 Jan 2005
Posts: 137
Location: NJ
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

Show Tags

New post 01 Mar 2005, 15:07
MA wrote:
700Plus wrote:
How would you solve it if the percentage of rain likely on any days is 30% as against the given 50%( or 1/2).

Assuming your addition is a contineuation of the original question.
=7C4 * (3/10)^7 =(35x2187)/10^7


Using the following:

nPk = nCk * p^k * (1-p) ^ (n-k)
where nPk denotes the probability of an event having a given outcome exactly k times in n tests, p is the probability of the event having this outcome in each single test, and nCk comes from Combinations Theory.

it should be 7C4 * (3/10)^4 * (7/10)^3 iSN'T IT??????

CAN SOMEBODY TELL ME WHETHER I AM RIGHT OR WRONG?????
Manager
Manager
avatar
Joined: 08 Oct 2004
Posts: 120
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

Show Tags

New post 01 Mar 2005, 15:46
1
Tajik4GMAT wrote:
General rule

x successes out of n trials :

P(x)=n!/x!*(n-x)!*(p)^x*(1-p)^n-x

Some stuff from my Stats. class :wink:

P.S. BTW this my first post :wink:


The way we solve it

7!/4!*(7-4)!*(1/2)^4*(1-1/2)^(7-4)

Am I right?
Senior Manager
Senior Manager
avatar
Joined: 19 Nov 2004
Posts: 418
Location: SF Bay Area, USA
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

Show Tags

New post 01 Mar 2005, 16:06
Quote:
MA wrote:
Yes, You guys are right. To add a twist to the problem:
a) What is the probablility that it would rain on 4 consequitive days out of the 7 consequtive days?

=7P4(1/2^7)


MA, Hint: we are looking for 4 consequitive days -> There are only 4 sets of consequitve days Days {1,2,3,4} , {2,3,4,5}, {3,4,5,6}, {4,5,6,7}

Also, we don't care if it rains on the other 3 days or not.

Quote:
MA wrote:
b) What is the probablility that it would rain on only 3 alternate days out of the 7 consequtive days?

=3*(1/2)^7 ??????????

MA, Hint: 3 Alternate days are Days {1,3,5} or { 2,4,6} or {3,5,7}
Here, we don't want rain on other days.

Quote:
MA wrote:

c) If it rains on the day before, the probability of it raining the next day becomes 1/4. What is the probability that it rains on 4 days out of 7 consecutive days in Rwanda?


=7C4 (1/2) (1/2*1/4) (1/2*1/4*1/4) (1/2*1/4*1/4*1/4)
=7C4 (1/2) (1/8) (1/32) (1/128)
=7C4 (1/2) (1/2)^3 (1/2)^5 (1/2)^7
=7C4 (1/2)^16


Hint: We cannot use Binomial eqn here as the probabilities are dependant.
This one is definitely complicated - we may need to consider different cases such as consequitve days or alternate days and come up an answer.
I am sure somebody will solve this one.
Manager
Manager
avatar
Joined: 13 Oct 2004
Posts: 202
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

Show Tags

New post 01 Mar 2005, 16:27
1
a) What is the probablility that it would rain on 4 consequitive days out of the 7 consequtive days?

4C1/(2)^7= 4/128 = 1/32

b) What is the probablility that it would rain on only 3 alternate days out of the 7 consequtive days?

3/128

c) If it rains on the day before, the probability of it raining the next day becomes 1/4. What is the probability that it rains on 4 days out of 7 consecutive days in Rwanda?

= 1 * 1/(2)^4 + 4 * (1/2 * 1/4)*(1/2^2) + 8 * (1/2 * 1/4 * 1/4) * 1/2 + 4 ( 1/2 * 1/4 * 1/4 * 1/4) = 11/32 ?.

there are 4 days of rain: 1 - it rains alternate days. 2 - it rains 2 consecutive days and 2 other days non consecutive 3 - it rains 3 days consec and 1 day non consec and 4 - it rains consec. Sum each of these probs to get the total prob. Not sure if this is the right approach, but thats my shot.
Manager
Manager
avatar
Joined: 13 Oct 2004
Posts: 202
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

Show Tags

New post 02 Mar 2005, 06:54
a) What is the probablility that it would rain on 4 consequitive days out of the 7 consequtive days?

4/7C4 ?

b) What is the probablility that it would rain on only 3 alternate days out of the 7 consequtive days?

3/2^5 ?
SVP
SVP
User avatar
Joined: 03 Jan 2005
Posts: 1702
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

Show Tags

New post 02 Mar 2005, 11:57
Ok, let me try this out too.

nocilis wrote:

a) What is the probablility that it would rain on 4 consequitive days out of the 7 consequtive days?

Total outcome: 2^7
Possible outcomes for 4 consequitive days: 4 (1234, 2345, 3456, 4567)
Probability =4/2^7

Quote:
b) What is the probablility that it would rain on only 3 alternate days out of the 7 consequtive days?

Possible outcomes: 3 (135, 246, 357)
Probability=3/2^7

Quote:
c) If it rains on the day before, the probability of it raining the next day becomes 1/4. What is the probability that it rains on 4 days out of 7 consecutive days in Rwanda?

I don't know how to do this one. Anybody?
Senior Manager
Senior Manager
avatar
Joined: 19 Nov 2004
Posts: 418
Location: SF Bay Area, USA
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

Show Tags

New post 05 Mar 2005, 13:04
1
Thanks for reminding about this thread.
I made these questions up, so there is no official answer.

My answer:
a) What is the probablility that it would rain on 4 consequitive days out of the 7 consequtive days?
There are only 4 sets of consequitve days Days {1,2,3,4} , {2,3,4,5}, {3,4,5,6}, {4,5,6,7}

=4/ 2^7

b) What is the probablility that it would rain on only 3 alternate days out of the 7 consequtive days?
3 Alternate days are Days {1,3,5} or { 2,4,6} or {3,5,7}

= 3/2^7

c) If it rains on the day before, the probability of it raining the next day becomes 1/4. What is the probability that it rains on 4 days out of 7 consecutive days in Rwanda?

I think this one is tough, perhaps out of scope for GMAT - I will solve this one as time permits. As of now I don't have an answer.
VP
VP
avatar
Joined: 18 Nov 2004
Posts: 1154
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

Show Tags

New post 05 Mar 2005, 18:24
HongHu wrote:
Ok, let me try this out too.

nocilis wrote:

a) What is the probablility that it would rain on 4 consequitive days out of the 7 consequtive days?

Total outcome: 2^7
Possible outcomes for 4 consequitive days: 4 (1234, 2345, 3456, 4567)
Probability =4/2^7

Quote:
b) What is the probablility that it would rain on only 3 alternate days out of the 7 consequtive days?

Possible outcomes: 3 (135, 246, 357)
Probability=3/2^7

Quote:
c) If it rains on the day before, the probability of it raining the next day becomes 1/4. What is the probability that it rains on 4 days out of 7 consecutive days in Rwanda?

I don't know how to do this one. Anybody?


q3---let's see, out of 4 possibilities 1234, 2345, 3456, 4567....

each scenario has p(e) = (1/2*1/4*1/4*1/4*1/2*1/2)

so p(e) = 4(1/2*1/4*1/4*1/4*1/2*1/2) = 1/128
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2815
Re: In Rwanda, the chance for rain on any given day is 1/2. What  [#permalink]

Show Tags

New post 12 Oct 2017, 18:07
nocilis wrote:
In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 4 out of 7 consecutive days in Rwanda?

A. 4/7
B. 3/7
C. 35/128
D. 4/28
E. 28/135


We can let R denote rain and N denote no rain; thus, we need to determine:

P(R-R-R-R-N-N-N) = (1/2)^7 = 1/128

However, there are 7C4 = 7!/(4! x 3!) = (7 x 6 x 5)/(3 x 2) = 35 ways to organize the letters R-R-R-R-N-N-N, so the total probability is 35 x 1/128 = 35/128.

Answer: C
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: In Rwanda, the chance for rain on any given day is 1/2. What   [#permalink] 12 Oct 2017, 18:07

Go to page    1   2    Next  [ 21 posts ] 

Display posts from previous: Sort by

In Rwanda, the chance for rain on any given day is 1/2. What

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne