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# What is the probability that the sum of two different single-digit pri

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Math Expert
Joined: 02 Sep 2009
Posts: 58320
What is the probability that the sum of two different single-digit pri  [#permalink]

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05 Feb 2019, 02:14
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Difficulty:

45% (medium)

Question Stats:

61% (01:37) correct 39% (01:43) wrong based on 31 sessions

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What is the probability that the sum of two different single-digit prime numbers will NOT be prime?

A. 0
B. 1/2
C. 2/3
D. 5/6
E. 1

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Re: What is the probability that the sum of two different single-digit pri  [#permalink]

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05 Feb 2019, 02:22
Bunuel wrote:
What is the probability that the sum of two different single-digit prime numbers will NOT be prime?

A. 0
B. 1/2
C. 2/3
D. 5/6
E. 1

The single digit primes are 2, 3 , 5 & 7. 4C2 , i.e. 6 numbers which can be formed with sum of any two 2 of these. Prime number is necessarily an odd number. Hence, any number made with any 2 of 3,5 or 7 can not be prime. Hence, possible prime numbers can be formed with only 2 + 3, 2+5 or 2+7. Out of these 2+7 = 9 which is not a prime.

Hence, only 2 numbers are prime of the 6 numbers. Hence the answer is (6-2)/6 = 2/3
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Re: What is the probability that the sum of two different single-digit pri  [#permalink]

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05 Feb 2019, 05:15
Bunuel wrote:
What is the probability that the sum of two different single-digit prime numbers will NOT be prime?

A. 0
B. 1/2
C. 2/3
D. 5/6
E. 1

prime digits = 2,3,5,7 = total sum combinations 4c2 = 6
sum which wont be prime = 2+7, 3+5,3+7 ,7+5 = 4

4/6 ; 2/3
IMO C
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Re: What is the probability that the sum of two different single-digit pri  [#permalink]

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08 Feb 2019, 09:16
Bunuel wrote:
What is the probability that the sum of two different single-digit prime numbers will NOT be prime?

A. 0
B. 1/2
C. 2/3
D. 5/6
E. 1

There are 4 single-digit prime numbers: 2, 3, 5, and 7. Therefore, the number of ways to choose any 2 of them is 4C2 = (4 x 3)/2 = 6. The ways that the sum of a pair of these 4 numbers is a prime are: (2, 3) and (2, 5). Therefore, 4 out of the 6 ways the sum will not be a prime, and hence the probability is 4/6 = 2/3.

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Re: What is the probability that the sum of two different single-digit pri   [#permalink] 08 Feb 2019, 09:16
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