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M23-22

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M23-22 [#permalink]

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New post 16 Sep 2014, 01:19
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If two different numbers are randomly selected from set \(\{1, 2, 3, 4, 5\}\), what is the probability that the sum of the two numbers is greater than 4?

A. \(\frac{3}{5}\)
B. \(\frac{7}{10}\)
C. \(\frac{4}{5}\)
D. \(\frac{9}{10}\)
E. \(\frac{19}{20}\)

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Re M23-22 [#permalink]

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New post 16 Sep 2014, 01:19
2
Official Solution:

If two different numbers are randomly selected from set \(\{1, 2, 3, 4, 5\}\), what is the probability that the sum of the two numbers is greater than 4?

A. \(\frac{3}{5}\)
B. \(\frac{7}{10}\)
C. \(\frac{4}{5}\)
D. \(\frac{9}{10}\)
E. \(\frac{19}{20}\)


Let's find the probability of the opposite event and subtract that value from 1. The opposite event would be if we choose 2 different number so that their sum will be less or equal to 4.

The number of total outcomes is \(C^2_5=10\) (choosing 2 different numbers from the set of 5 different numbers);

The number of outcomes when \(sum\leq{4}\) is 2: only (1,2) and (1,3);

\(P=1-\frac{2}{10}=\frac{4}{5}\).


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: M23-22 [#permalink]

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New post 11 Jun 2016, 10:52
Bunuel wrote:
Official Solution:

If two different numbers are randomly selected from set \(\{1, 2, 3, 4, 5\}\), what is the probability that the sum of the two numbers is greater than 4?

A. \(\frac{3}{5}\)
B. \(\frac{7}{10}\)
C. \(\frac{4}{5}\)
D. \(\frac{9}{10}\)
E. \(\frac{19}{20}\)


Let's find the probability of the opposite event and subtract that value from 1. The opposite event would be if we choose 2 different number so that their sum will be less or equal to 4.

The number of total outcomes is \(C^2_5=10\) (choosing 2 different numbers from the set of 5 different numbers);

The number of outcomes when \(sum\leq{4}\) is 2: only (1,2) and (1,3);

\(P=1-\frac{2}{10}=\frac{4}{5}\).


Answer: C


Thank you for this great questions, gmat club is really good!
This said,
why do I have only 2 possible outcomes? (1,2) and (1,3).. why doesn't (2,1) and (3,1) work? I can randomly select them in this order as well?

:?
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Re: M23-22 [#permalink]

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New post 11 Aug 2016, 04:21
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By definition a subset contains only different elements of the subset. So {1,2} and {2,1} is the same subset.
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Re: M23-22 [#permalink]

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New post 04 Jul 2017, 08:35
[/m]
Bunuel wrote:
Official Solution:

If two different numbers are randomly selected from set \(\{1, 2, 3, 4, 5\}\), what is the probability that the sum of the two numbers is greater than 4?

A. \(\frac{3}{5}\)
B. \(\frac{7}{10}\)
C. \(\frac{4}{5}\)
D. \(\frac{9}{10}\)
E. \(\frac{19}{20}\)


Let's find the probability of the opposite event and subtract that value from 1. The opposite event would be if we choose 2 different number so that their sum will be less or equal to 4.

The number of total outcomes is \(C^2_5=10\) (choosing 2 different numbers from the set of 5 different numbers);

The number of outcomes when \(sum\leq{4}\) is 2: only (1,2) and (1,3);

\(P=1-\frac{2}{10}=\frac{4}{5}\).


Answer: C


The answer is wrong
\(P=1-\frac{2}{10}=\frac{8}{5}\). and not\(\frac{4}{5}\)
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Re: M23-22 [#permalink]

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New post 04 Jul 2017, 08:37
pranab223 wrote:
[/m]
Bunuel wrote:
Official Solution:

If two different numbers are randomly selected from set \(\{1, 2, 3, 4, 5\}\), what is the probability that the sum of the two numbers is greater than 4?

A. \(\frac{3}{5}\)
B. \(\frac{7}{10}\)
C. \(\frac{4}{5}\)
D. \(\frac{9}{10}\)
E. \(\frac{19}{20}\)


Let's find the probability of the opposite event and subtract that value from 1. The opposite event would be if we choose 2 different number so that their sum will be less or equal to 4.

The number of total outcomes is \(C^2_5=10\) (choosing 2 different numbers from the set of 5 different numbers);

The number of outcomes when \(sum\leq{4}\) is 2: only (1,2) and (1,3);

\(P=1-\frac{2}{10}=\frac{4}{5}\).


Answer: C


The answer is wrong
\(P=1-\frac{2}{10}=\frac{8}{5}\). and not\(\frac{4}{5}\)


Really? Check again, please.
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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

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.


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Re: M23-22 [#permalink]

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New post 04 Jul 2017, 09:07
Bunuel wrote:
pranab223 wrote:
[/m]
Bunuel wrote:
Official Solution:

If two different numbers are randomly selected from set \(\{1, 2, 3, 4, 5\}\), what is the probability that the sum of the two numbers is greater than 4?

A. \(\frac{3}{5}\)
B. \(\frac{7}{10}\)
C. \(\frac{4}{5}\)
D. \(\frac{9}{10}\)
E. \(\frac{19}{20}\)


Let's find the probability of the opposite event and subtract that value from 1. The opposite event would be if we choose 2 different number so that their sum will be less or equal to 4.

The number of total outcomes is \(C^2_5=10\) (choosing 2 different numbers from the set of 5 different numbers);

The number of outcomes when \(sum\leq{4}\) is 2: only (1,2) and (1,3);

\(P=1-\frac{2}{10}=\frac{4}{5}\).


Answer: C


The answer is wrong
\(P=1-\frac{2}{10}=\frac{8}{5}\). and not\(\frac{4}{5}\)


Really? Check again, please.

You are right its \(\frac{4}{5}\)
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Re: M23-22 [#permalink]

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New post 16 Jul 2017, 00:42
How is it not B =7/10?

When you consider the case , how many pairs of numbers whose sum is greater than 4, you get

(1,4),(1,5).(2,4),(2,5),(2,3),(3,4),(3,5),(4,5) which is 7 outcomes out of total possible 10 outcomes.

Please explain.
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Re: M23-22 [#permalink]

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New post 16 Jul 2017, 04:12
ajanpaul wrote:
How is it not B =7/10?

When you consider the case , how many pairs of numbers whose sum is greater than 4, you get

(1,4),(1,5).(2,4),(2,5),(2,3),(3,4),(3,5),(4,5) which is 7 outcomes out of total possible 10 outcomes.

Please explain.


It's not that hard to do the following:
1 - (1,4)
2 - (1,5)
3 - (2,4)
4 - (2,5)
5 - (2,3)
6 - (3,4)
7 - (3,5)
8 - (4,5)
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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?
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Re: M23-22 [#permalink]

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New post 15 Mar 2018, 09:25
Only (1,2) and (1,3) are less than or equal to 4. The required probability is 1-(2/5C2). The answer is 4/5.
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Re: M23-22 [#permalink]

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New post 30 Jun 2018, 12:55
When you say 2 different numbers are randomly selected from set means it cannot be {1,1}, {2,2}, {3,3}, {4,4}, and {5,5}.
But it can be {1,2} or {2,1}.

The question should clearly indicate that subsets have to be different.

Thanks.
Re: M23-22   [#permalink] 30 Jun 2018, 12:55
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