GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 17 Jan 2020, 12:48

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

The high temperature of a summer day on Fire Island is always one of

  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: 14 Aug 2006
Posts: 296
The high temperature of a summer day on Fire Island is always one of  [#permalink]

Show Tags

New post 26 Sep 2006, 10:13
9
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

24% (03:02) correct 76% (02:12) wrong based on 88 sessions

HideShow timer Statistics

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?


A. 1/27

B. 2/9

C. 1/3

D. 4/9

E. 13/27
Most Helpful Expert Reply
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9983
Location: Pune, India
Re: The high temperature of a summer day on Fire Island is always one of  [#permalink]

Show Tags

New post 15 Jul 2011, 00:19
6
2
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

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
General Discussion
Manager
Manager
User avatar
Joined: 25 May 2006
Posts: 161
Re: The high temperature of a summer day on Fire Island is always one of  [#permalink]

Show Tags

New post 26 Sep 2006, 10:36
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
Senior Manager
Senior Manager
avatar
Joined: 15 Jul 2006
Posts: 373
Re: The high temperature of a summer day on Fire Island is always one of  [#permalink]

Show Tags

New post 26 Sep 2006, 11:09
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: 323
Re: The high temperature of a summer day on Fire Island is always one of  [#permalink]

Show Tags

New post 26 Sep 2006, 11:29
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: 296
Re: The high temperature of a summer day on Fire Island is always one of  [#permalink]

Show Tags

New post 26 Sep 2006, 13:04
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: 112
Re: The high temperature of a summer day on Fire Island is always one of  [#permalink]

Show Tags

New post 26 Sep 2006, 23:45
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: 94
Re: The high temperature of a summer day on Fire Island is always one of  [#permalink]

Show Tags

New post 14 Jul 2011, 13:45
Can some expert explain this question pls?
Manager
Manager
User avatar
Status: On...
Joined: 16 Jan 2011
Posts: 154
Re: The high temperature of a summer day on Fire Island is always one of  [#permalink]

Show Tags

New post 16 Jul 2011, 11:04
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
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9032
Location: United States (CA)
Re: The high temperature of a summer day on Fire Island is always one of  [#permalink]

Show Tags

New post 19 Apr 2019, 10:37
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?


A. 1/27

B. 2/9

C. 1/3

D. 4/9

E. 13/27


Since each day has 3 possible outcomes for the high temperature, 3 consecutive days have 3 x 3 x 3 = 27 total possible outcomes for the high temperature. The number of ways to get 85 as a median can occur in the following ways:

One reading of 84, two readings of 85: By the permutations of indistinguishable objects formula, this can occur in 3!/2! = 3 ways. (which are (84, 84, 85), (84, 85, 84); (85, 84, 84)).

One reading of 86, two readings of 85: This can also occur in 3 ways, as explained above.

One reading of each temperature: This can occur in 3! = 6 ways.

Three readings of 85: This can occur in one way.

Thus, a median high temperature of 85 degrees occurs in 3 + 3 + 6 + 1 = 13 outcomes. Thus, the probability is 13/27.

Answer: E
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
181 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: The high temperature of a summer day on Fire Island is always one of   [#permalink] 19 Apr 2019, 10:37
Display posts from previous: Sort by

The high temperature of a summer day on Fire Island is always one of

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





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