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M24-27

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M24-27 [#permalink]

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New post 16 Sep 2014, 01:22
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Question Stats:

64% (01:23) correct 36% (02:13) wrong based on 28 sessions

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20 throws of a die produces following results:

Image

What is the probability that one more throw to this series will increase the mean score?


A. \(\frac{1}{6}\)
B. \(\frac{1}{3}\)
C. \(\frac{1}{2}\)
D. \(\frac{2}{3}\)
E. \(\frac{5}{6}\)
[Reveal] Spoiler: OA

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Re M24-27 [#permalink]

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New post 16 Sep 2014, 01:22
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Official Solution:


20 throws of a die produces following results:

Image

What is the probability that one more throw to this series will increase the mean score?


A. \(\frac{1}{6}\)
B. \(\frac{1}{3}\)
C. \(\frac{1}{2}\)
D. \(\frac{2}{3}\)
E. \(\frac{5}{6}\)

Current mean score = \(\frac{1*4 + 2*3 + 3*5 + 4*2 + 5*2 + 6*4}{20} = \frac{67}{20} = 3.35\). Only the fall of 4, 5, or 6 will increase the mean score of the series.

Answer: C
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: M24-27 [#permalink]

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Bunuel wrote:
Official Solution:


20 throws of a die produces following results:

Image

What is the probability that one more throw to this series will increase the mean score?


Both the scores 1 and 6 have occurrences of 4, they cancel out to an average of 3.5 with half the roll outcomes increasing the mean score.

To save time we can average scores 2-5, or we can reason that since scores 4 and 5 have a total of 4 occurrences, while score 2 only has 3 occurrences, that the average will be just a bit greater than 3, and that only rolling 4, 5, and 6 will increase the average.

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Re: M24-27 [#permalink]

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New post 22 Dec 2016, 21:39
Hi,
Can you please explain in more detail please?I have not understood clearly.

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Re: M24-27 [#permalink]

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New post 23 Dec 2016, 01:30
Bunuel wrote:
20 throws of a die produces following results:

Image

What is the probability that one more throw to this series will increase the mean score?


A. \(\frac{1}{6}\)
B. \(\frac{1}{3}\)
C. \(\frac{1}{2}\)
D. \(\frac{2}{3}\)
E. \(\frac{5}{6}\)


The average score now is \(\frac{total \ score}{# \ of \ throws}=\frac{1*4+2*3+3*5+4*2+5*2+6*4}{20}=\frac{67}{20}=3.something\).

Now, the average score will increase if we get more than the current average, so if we get 4, 5, or 6 on the next throw. The probability of that is 3/6=1/2.

Answer: C.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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M24-27 [#permalink]

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New post 02 Oct 2017, 07:31
Bunuel wrote:
Bunuel wrote:
20 throws of a die produces following results:

Image

What is the probability that one more throw to this series will increase the mean score?


A. \(\frac{1}{6}\)
B. \(\frac{1}{3}\)
C. \(\frac{1}{2}\)
D. \(\frac{2}{3}\)
E. \(\frac{5}{6}\)


The average score now is \(\frac{total \ score}{# \ of \ throws}=\frac{1*4+2*3+3*5+4*2+5*2+6*4}{20}=\frac{67}{20}=3.something\).


Now, the average score will increase if we get more than the current average, so if we get 4, 5, or 6 on the next throw. The probability of that is 3/6=1/2.

Answer: C.



Bunuel

Isn't it like whenever we throw the outcome will have the result of increasing the mean,coz whenever a number is added to the set the mean,the mean will eventually increase.Suppose in this cast if the mean is 3.something and if 1or 2 or 3 is added then eventually it will not decrease the mean.
For instance if 1 is added to the set then it will become 68/20 which is 3.4>3.35(original)

Please correct my understanding...!!

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Re: M24-27 [#permalink]

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New post 02 Oct 2017, 11:30
himanshukamra2711 wrote:
Bunuel wrote:
Bunuel wrote:
20 throws of a die produces following results:

Image

What is the probability that one more throw to this series will increase the mean score?


A. \(\frac{1}{6}\)
B. \(\frac{1}{3}\)
C. \(\frac{1}{2}\)
D. \(\frac{2}{3}\)
E. \(\frac{5}{6}\)


The average score now is \(\frac{total \ score}{# \ of \ throws}=\frac{1*4+2*3+3*5+4*2+5*2+6*4}{20}=\frac{67}{20}=3.something\).


Now, the average score will increase if we get more than the current average, so if we get 4, 5, or 6 on the next throw. The probability of that is 3/6=1/2.

Answer: C.



Bunuel

Isn't it like whenever we throw the outcome will have the result of increasing the mean,coz whenever a number is added to the set the mean,the mean will eventually increase.Suppose in this cast if the mean is 3.something and if 1or 2 or 3 is added then eventually it will not decrease the mean.
For instance if 1 is added to the set then it will become 68/20 which is 3.4>3.35(original)

Please correct my understanding...!!


After one more throw the number of occurrences will be 21, not 20: 68/21 = ~3.24 < 3.35.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128688 [0], given: 12182

Re: M24-27   [#permalink] 02 Oct 2017, 11:30
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