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

It is currently 17 Sep 2014, 11:49

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

The high temperature of a summer day on Fire Island is

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
avatar
Joined: 14 Aug 2006
Posts: 368
Followers: 1

Kudos [?]: 3 [0], given: 0

GMAT Tests User
The high temperature of a summer day on Fire Island is [#permalink] New post 26 Sep 2006, 09:13
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 100% (01:47) wrong based on 5 sessions
The high temperature of a summer day on Fire Island is always one of three temperatures: 84, 85 or 86 degrees. If there is an equal chance of each temperature, what is the probability that the median high temperature over a three day period will be 85 degrees?


1) 1/27

2) 2/9

3) 1/3

4) 4/9

5) 13/27
Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4766
Location: Pune, India
Followers: 1112

Kudos [?]: 5041 [1] , given: 164

Re: PS - Probability [#permalink] New post 14 Jul 2011, 23:19
1
This post received
KUDOS
Expert's post
gk3.14 wrote:
The high temperature of a summer day on Fire Island is always one of three temperatures: 84, 85 or 86 degrees. If there is an equal chance of each temperature, what is the probability that the median high temperature over a three day period will be 85 degrees?


1) 1/27

2) 2/9

3) 1/3

4) 4/9

5) 13/27


When we are asked to find the median of 3 numbers, we arrange them in increasing order and then pick the middle number.
The median of 85 will be obtained when the temperatures are one of:
{85, 85, 85}
{85, 86, 86}
{84, 85, 85}
{84, 85, 86}

When will the temperatures be {85, 85, 85}?
When every day the high is 85. What is the probability of this happening? 1/3 * 1/3 * 1/3 = 1/27

When will the temperatures be {85, 85, 86}?
When the high is 85 on two days and 86 on another. What is the probability of this happening? Probability of 85 on first day is 1/3. Of 85 on second day is 1/3 and of 86 on third day is 1/3. Probability of this is 1/3 * 1/3 * 1/3 = 1/27. There are other ways in which you can get 85, 85, 86. e.g. 86 on first day, 85 on other two. Another way is 86 on second day and 85 on other two. So basically we are looking for the number of ways in which we can arrange 85, 85, 86 among 3 days. This can be done in 3!/2! = 3 ways.
Probability of getting {85, 85, 86} is 1/27 * 3 = 1/9

Similarly, probability of getting {84, 85, 85} is also 1/9.

Probability of getting {84, 85, 86} will be 1/3 * 1/3 * 1/3 * 3! = 6/27

Total probability of getting median 85 = 1/27 + 1/9 + 1/9 + 6/27 = 13/27
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Manager
Manager
User avatar
Joined: 25 May 2006
Posts: 227
Followers: 1

Kudos [?]: 14 [0], given: 0

GMAT Tests User
 [#permalink] New post 26 Sep 2006, 09:36
1/3?

84-85-86, lets simplify --> 4-5-6

There are 27 possible combinations, 9 out of 27 can have 5 as median.
9/27 --> 1/3
_________________

Who is John Galt?

Senior Manager
Senior Manager
avatar
Joined: 15 Jul 2006
Posts: 382
Followers: 1

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

GMAT Tests User
 [#permalink] New post 26 Sep 2006, 10:09
probailities:
day 1 (any temperature) = 3/3
day 2 (85 only) = 1/3
day 1 (any temperature) = 3/3

so 3/3 x 1/3 x 3/3 =9/27 = 1/3
Senior Manager
Senior Manager
User avatar
Joined: 05 Mar 2006
Posts: 348
Followers: 1

Kudos [?]: 5 [0], given: 0

GMAT Tests User
 [#permalink] New post 26 Sep 2006, 10:29
Total number of ways:P 3*3*3 = 27

Possible permutations as 85 median

(85, 85, 85), or any permutation of all three.

Total number of permutations: 3 + (3*2*1) = 9

Therefore, 9/27 = 1/3
Senior Manager
Senior Manager
avatar
Joined: 14 Aug 2006
Posts: 368
Followers: 1

Kudos [?]: 3 [0], given: 0

GMAT Tests User
 [#permalink] New post 26 Sep 2006, 12:04
That is what I got too.. but the answer is apparently : 13/27

Here is the OE..
First, lets figure out the different ways we could get a median of 85: 84, 85, 86; 84, 85, 85; 85, 85, 86; and 85, 85, 85. Now the probability of 84, 85, 86 is 1/3 * 1/3*/13 = 1/27 This arrangement could occur in 6 different ways (there are three days where the 84 could go, two where the 85 could go, and one for the 86: (3)(2)(1) = 6), giving us a probability of 1/27 * 6/1 = 2/9. Now the probability of 84, 85, 85 is 1/3, 1/3, 1/3 = 1/27 and there are 3 different ways to arrange the temperatures (the 84 could occur on three days, the other two days are 85), so the probability is 1/27 * 3/1 = 1/9. Similarly, the 85, 85, 86 is has a probability of 1/27 * 3/1 = 1/9. Finally, the probability of 85, 85, 85 is 1/3* 1/3*1/3 = 1/27 . To find the probability of a median of 85, we add up the probabilities of each of the scenarios: 2/9 + 1/9 + 1/9 + 1/27 . The correct answer is E.
Manager
Manager
avatar
Joined: 25 Sep 2006
Posts: 153
Followers: 1

Kudos [?]: 3 [0], given: 0

 [#permalink] New post 26 Sep 2006, 22:45
Hmm, we missed the fact that

median of (4,5,5),(6,5,5)... is 5

A good lesson
Manager
Manager
avatar
Joined: 23 Jan 2011
Posts: 128
Followers: 1

Kudos [?]: 10 [0], given: 12

Re: PS - Probability [#permalink] New post 14 Jul 2011, 12:45
Can some expert explain this question pls?
Manager
Manager
User avatar
Status: On...
Joined: 16 Jan 2011
Posts: 189
Followers: 3

Kudos [?]: 35 [0], given: 62

GMAT Tests User
Re: PS - Probability [#permalink] New post 16 Jul 2011, 10:04
Good question and equally good explanation, Karishma.....Thanks!!!
But I think there was a spell-mistake in the explanation...
VeritasPrepKarishma wrote:
gk3.14 wrote:
The high temperature of a summer day on Fire Island is always one of three temperatures: 84, 85 or 86 degrees. If there is an equal chance of each temperature, what is the probability that the median high temperature over a three day period will be 85 degrees?


1) 1/27

2) 2/9

3) 1/3

4) 4/9

5) 13/27


When we are asked to find the median of 3 numbers, we arrange them in increasing order and then pick the middle number.
The median of 85 will be obtained when the temperatures are one of:
{85, 85, 85}
{85, 86, 86}{85, 85, 86}
{84, 85, 85}
{84, 85, 86}

When will the temperatures be {85, 85, 85}?
When every day the high is 85. What is the probability of this happening? 1/3 * 1/3 * 1/3 = 1/27

When will the temperatures be {85, 85, 86}?
When the high is 85 on two days and 86 on another. What is the probability of this happening? Probability of 85 on first day is 1/3. Of 85 on second day is 1/3 and of 86 on third day is 1/3. Probability of this is 1/3 * 1/3 * 1/3 = 1/27. There are other ways in which you can get 85, 85, 86. e.g. 86 on first day, 85 on other two. Another way is 86 on second day and 85 on other two. So basically we are looking for the number of ways in which we can arrange 85, 85, 86 among 3 days. This can be done in 3!/2! = 3 ways.
Probability of getting {85, 85, 86} is 1/27 * 3 = 1/9

Similarly, probability of getting {84, 85, 85} is also 1/9.

Probability of getting {84, 85, 86} will be 1/3 * 1/3 * 1/3 * 3! = 6/27

Total probability of getting median 85 = 1/27 + 1/9 + 1/9 + 6/27 = 13/27

_________________

Labor cost for typing this post >= Labor cost for pushing the Kudos Button
kudos-what-are-they-and-why-we-have-them-94812.html

Re: PS - Probability   [#permalink] 16 Jul 2011, 10:04
    Similar topics Author Replies Last post
Similar
Topics:
Dartmouth Tuck Summer Visit Day yevgeniy11223 10 01 Jun 2012, 08:25
If a latter-day Robinson Crusoe was marooned on an island garimavyas 0 26 Mar 2014, 12:29
1 Temperature Acer86 1 18 Apr 2011, 01:42
18 If a latter-day Robinson Crusoe was marooned on an island neeshpal 52 15 Mar 2009, 08:33
During the 365 days of a certain year, all the temperatures ruhi 4 14 Nov 2004, 13:22
Display posts from previous: Sort by

The high temperature of a summer day on Fire Island is

  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®.