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Set S consists of all prime numbers less than 10. If two num [#permalink]

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11 Jan 2013, 11:45

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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?

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 \(= 3/6 = 1/2\)

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]

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11 Jan 2013, 13:51

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).

Re: Set S consists of all prime numbers less than 10. If two num [#permalink]

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24 Dec 2015, 23:50

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