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# What is the probability that the sum of two different

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What is the probability that the sum of two different [#permalink]  27 Feb 2019, 21:38
Expert's post
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Question Stats:

60% (01:09) correct 40% (02:03) wrong based on 15 sessions
What is the probability that the sum of two different single-digit prime numbers will NOT be prime?

(A) 0

(B) $$\frac{1}{2}$$

(C) $$\frac{2}{3}$$

(D) $$\frac{5}{6}$$

(E) 1

Diagnostic # 11
[Reveal] Spoiler: OA

_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

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Re: What is the probability that the sum of two different [#permalink]  28 Feb 2019, 10:11
1
KUDOS
Expert's post
chetan2u wrote:
What is the probability that the sum of two different single-digit prime numbers will NOT be prime?
(A) 0

(B) $$\frac{1}{2}$$

(C) $$\frac{2}{3}$$

(D) $$\frac{5}{6}$$

(E) 1

Diagnostic # 11

Single-digit prime numbers: 2, 3, 5, 7

Since there are so few numbers, we can list all 6 possible combinations.

#1) 2 & 3 (sum = 5)
#2) 2 & 5 (sum = 7)
#3) 2 & 7 (sum = 9)
#4) 3 & 5 (sum = 8)
#5) 3 & 7 (sum = 10)
#6) 5 & 7 (sum = 12)

Of the 6 possible outcomes, 4 outcomes yield a NON-PRIME sum

P(sum is NOT prime) = 4/6 = 2/3

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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Re: What is the probability that the sum of two different [#permalink]  12 Jun 2019, 02:16
1
KUDOS
chetan2u wrote:
What is the probability that the sum of two different single-digit prime numbers will NOT be prime?

(A) 0

(B) $$\frac{1}{2}$$

(C) $$\frac{2}{3}$$

(D) $$\frac{5}{6}$$

(E) 1

Diagnostic # 11

-------CONCEPT------------

Single digit prime numbers are
2,3,5,7

Now, except 2 all are odd so we can only get an odd sum if one of our prime number is even while other is odd (Only an odd number can be prime).

2+3 = 5
2+5 = 7
are only 2 cases to satisfy the condition.
while 2 + 7 = 9, it is not prime

& Now the total cases to get a sum by selecting any 2 prime numbers out of these 4 are 4C2 = 6

So, probability for sum NOT to be prime number = 4/6 = 2/3
Re: What is the probability that the sum of two different   [#permalink] 12 Jun 2019, 02:16
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