Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 14 Aug 2006
Posts: 296

The high temperature of a summer day on Fire Island is always one of
[#permalink]
Show Tags
26 Sep 2006, 10:13
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
Official Answer and Stats are available only to registered users. Register/ Login.




Veritas Prep GMAT Instructor
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
15 Jul 2011, 00:19
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 >




Manager
Joined: 25 May 2006
Posts: 161

Re: The high temperature of a summer day on Fire Island is always one of
[#permalink]
Show Tags
26 Sep 2006, 10:36
1/3?
848586, lets simplify > 456
There are 27 possible combinations, 9 out of 27 can have 5 as median.
9/27 > 1/3



Senior Manager
Joined: 15 Jul 2006
Posts: 373

Re: The high temperature of a summer day on Fire Island is always one of
[#permalink]
Show Tags
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
Joined: 05 Mar 2006
Posts: 323

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

Re: The high temperature of a summer day on Fire Island is always one of
[#permalink]
Show Tags
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
Joined: 25 Sep 2006
Posts: 112

Re: The high temperature of a summer day on Fire Island is always one of
[#permalink]
Show Tags
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
Joined: 23 Jan 2011
Posts: 94

Re: The high temperature of a summer day on Fire Island is always one of
[#permalink]
Show Tags
14 Jul 2011, 13:45
Can some expert explain this question pls?



Manager
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
16 Jul 2011, 11:04
Good question and equally good explanation, Karishma.....Thanks!!! But I think there was a spellmistake 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
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
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
_________________
5star 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.




Re: The high temperature of a summer day on Fire Island is always one of
[#permalink]
19 Apr 2019, 10:37






