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Retired Moderator V
Joined: 27 Oct 2017
Posts: 1308
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
A cube with its sides numbered 1— 6 is rolled twice, first landing on  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 49% (02:25) correct 51% (02:18) wrong based on 82 sessions

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A cube with its sides numbered 1— 6 is rolled twice, first landing on a and then landing on b. If any roll of the cube yields an equal chance of landing on any of the numbers 1 — 6, what is the probability that a + b is prime?

A) 0

B) $$\frac{1}{12}$$

C) $$\frac{5}{12}$$

D) $$\frac{7}{18}$$

E) $$\frac{4}{9}$$

Weekly Quant Quiz #6 Question No 10

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Manager  G
Joined: 14 Jun 2018
Posts: 211
Re: A cube with its sides numbered 1— 6 is rolled twice, first landing on  [#permalink]

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Prime nos between 1-12 : 2 , 3 , 5 , 7, 11
for 2 : (1,1) : 1/6*1/6 = 1/36
3 : (2,1), (1,2): 2 * 1/6 * 1/6 = 1/18
5 : (1,4) and (2,3) = 4*1/6*1/6 = 2/18
7 : (1,6) , (2,5) , (3,4) = 6*1/6*1/6 = 3/18
11 : (6,5) = 2*1/6*1/6 = 1/18

Total = 15/36 = 5/12
Intern  B
Joined: 03 Dec 2017
Posts: 31
Re: A cube with its sides numbered 1— 6 is rolled twice, first landing on  [#permalink]

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total outcome 36
prime comb 15
2,3,5,7
3,5,7
5,7
5,7
7,11
7,11

hence -> 15/36 --> 5/12 (C)
Intern  B
Joined: 21 Aug 2018
Posts: 3
Re: A cube with its sides numbered 1— 6 is rolled twice, first landing on  [#permalink]

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Is it C?
This is how i approached the question. As I am not sure at all please let me know if there's a mistake.

If a=1, then possible outcomes of b to make a + b prime number is 1, 2, 4, 6 => p= (1/6)*(4/6)
then a=2, a=3 and go on.

I got 15/36 = 5/12
Intern  B
Joined: 18 Oct 2018
Posts: 4
Location: United States (TX)
GMAT 1: 640 Q48 V30 GPA: 3.89
Re: A cube with its sides numbered 1— 6 is rolled twice, first landing on  [#permalink]

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We can count starting from 1 adding every other number to it as long as it sums upto a prime number.
Like:-
1, 2, 3, 4, 5, 6
1+1=2
1+2=3
1+4=5
1+6=7
2+1=3
2+3=5
2+5=7
3+2=5
3+4=7
4+1=5
4+3=7.......so on
Total favorable outcomes are 15
and total outcomes are 36
So probability of two numbers adding upto a prime number is 15/36=5/12.

Hope I am right !
Director  P
Joined: 18 Dec 2017
Posts: 822
Location: United States (KS)
Re: A cube with its sides numbered 1— 6 is rolled twice, first landing on  [#permalink]

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Quote:
A cube with its sides numbered 1— 6 is rolled twice, first landing on a and then landing on b. If any roll of the cube yields an equal chance of landing on any of the numbers 1 — 6, what is the probability that a + b is prime?

A) 0

B) $$\frac{1}{12}$$

C) $$\frac{5}{12}$$

D) $$\frac{7}{18}$$

E) $$\frac{4}{9}$$

1 - 1/2/3/4/5/6
2,3,5,7

2 - 1/2/3/4/5/6
3,5,7

3 - 1/2/3/4/5/6
5,7

4 - 1/2/3/4/5/6
5,7

5 - 1/2/3/4/5/6
7,11

6 - 1/2/3/4/5/6
7,11

15/36
=5/12

Note: Since a and b are different in sequence so 7 in case 6 is different from 7 in case 5.

Thank you!
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You are missing on great learning if you don't know what this is: Project SC Butler Re: A cube with its sides numbered 1— 6 is rolled twice, first landing on   [#permalink] 02 Oct 2019, 08:13
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