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Set S consists of all prime numbers less than 10. If two num

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Set S consists of all prime numbers less than 10. If two num [#permalink] New post 11 Jan 2013, 12:45
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Set S consists of all prime numbers less than 10. If two numbers are chosen from et S at random, what is the probability that the product of these numbers will be greater than the product of the numbers which were not chosen?

A. 1/3
B. 2/3
C. 1/2
D. 7/10
E. 4/5
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Jan 2013, 13:35, edited 1 time in total.
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Re: Prime integer probability [#permalink] New post 11 Jan 2013, 13:00
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Prime integers below 10: 2, 3, 5, 7

Total outcomes: Number of ways you can choose 2 from 4 = 4C2= 6 pairs
No. of ways for Event: Pairs that will have products greater than product of pairs not selected i.e. (3,5), (3,7), (5,7) = 3 pairs

Probability = number of ways/Total outcomes = 3/6 = 1/2

Hence choice(C) is correct.
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Re: Set S consists of all prime numbers less than 10. If two num [#permalink] New post 11 Jan 2013, 13:37
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hitman5532 wrote:
Set S consists of all prime numbers less than 10. If two numbers are chosen from et S at random, what is the probability that the product of these numbers will be greater than the product of the numbers which were not chosen?

A. 1/3
B. 2/3
C. 1/2
D. 7/10
E. 4/5


S={2, 3, 5, 7}

The simplest way would be to realize that we choose half of the numbers (basically we divide the group of 4 into two smaller groups of 2) and since a tie is not possible then the probability that the product of the numbers in either of subgroup is more than that of in another is 1/2 (the probability doesn't favor any of two subgroups).

Answer: C.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rule #3: the name of a topic (subject field) MUST be the first 40 characters (~the first two sentences) of the question.
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Re: Set S consists of all prime numbers less than 10. If two num [#permalink] New post 11 Jan 2013, 14:51
Bunuel wrote:
hitman5532 wrote:
Set S consists of all prime numbers less than 10. If two numbers are chosen from et S at random, what is the probability that the product of these numbers will be greater than the product of the numbers which were not chosen?

A. 1/3
B. 2/3
C. 1/2
D. 7/10
E. 4/5


S={2, 3, 5, 7}

The simplest way would be to realize that we choose half of the numbers (basically we divide the group of 4 into two smaller groups of 2) and since a tie is not possible then the probability that the product of the numbers in either of subgroup is more than that of in another is 1/2 (the probability doesn't favor any of two subgroups).

Answer: C.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rule #3: the name of a topic (subject field) MUST be the first 40 characters (~the first two sentences) of the question.


Sorry about that, failed to remember that after reading the rules a while back.

This question was nice and simple when I don't make a stupid mistake and put 9 in with the set (doh!)
Re: Set S consists of all prime numbers less than 10. If two num   [#permalink] 11 Jan 2013, 14:51
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