Last visit was: 23 Jul 2024, 10:47 It is currently 23 Jul 2024, 10:47
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

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

SORT BY:
Tags:
Show Tags
Hide Tags
Manager
Joined: 14 Aug 2006
Posts: 227
Own Kudos [?]: 204 [22]
Given Kudos: 0
Tutor
Joined: 16 Oct 2010
Posts: 15140
Own Kudos [?]: 66810 [13]
Given Kudos: 436
Location: Pune, India
General Discussion
Manager
Joined: 25 May 2006
Posts: 112
Own Kudos [?]: 331 [0]
Given Kudos: 0
Senior Manager
Joined: 15 Jul 2006
Posts: 365
Own Kudos [?]: 5 [0]
Given Kudos: 0
Re: The high temperature of a summer day on Fire Island is always one of [#permalink]
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
Joined: 05 Mar 2006
Posts: 283
Own Kudos [?]: 18 [0]
Given Kudos: 0
Re: The high temperature of a summer day on Fire Island is always one of [#permalink]
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
Manager
Joined: 14 Aug 2006
Posts: 227
Own Kudos [?]: 204 [0]
Given Kudos: 0
Re: The high temperature of a summer day on Fire Island is always one of [#permalink]
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
Joined: 25 Sep 2006
Posts: 93
Own Kudos [?]: 15 [0]
Given Kudos: 0
Re: The high temperature of a summer day on Fire Island is always one of [#permalink]
Hmm, we missed the fact that

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

A good lesson
Manager
Joined: 23 Jan 2011
Posts: 83
Own Kudos [?]: 431 [0]
Given Kudos: 13
Re: The high temperature of a summer day on Fire Island is always one of [#permalink]
Can some expert explain this question pls?
Manager
Joined: 16 Jan 2011
Status:On...
Posts: 129
Own Kudos [?]: 216 [2]
Given Kudos: 62
Re: The high temperature of a summer day on Fire Island is always one of [#permalink]
2
Kudos
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
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19185
Own Kudos [?]: 22702 [3]
Given Kudos: 286
Location: United States (CA)
Re: The high temperature of a summer day on Fire Island is always one of [#permalink]
3
Kudos
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.

Director
Joined: 09 Aug 2017
Posts: 686
Own Kudos [?]: 426 [0]
Given Kudos: 778
Re: The high temperature of a summer day on Fire Island is always one of [#permalink]
I want to clear a doubt here.

Question ask that the median high temperature over three days will be 85. So should keep days temperature in order of day
or I can again rearrange the temperatures.

As you did.

I agree that (84,85, 86) can be arranged in 6 ways. But if that order matters to me then how in some case 85 can be median. For example,

order of temperature is 86 84, 85, then without rearrangement how median could be 85. And how could I consider such case for calculating the probability.
In your case you have considered rearrangement of temperatures.

ScottTargetTestPrep 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?

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.

Non-Human User
Joined: 09 Sep 2013
Posts: 34045
Own Kudos [?]: 853 [0]
Given Kudos: 0
Re: The high temperature of a summer day on Fire Island is always one of [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: The high temperature of a summer day on Fire Island is always one of [#permalink]
Moderator:
Math Expert
94592 posts