GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
A cube with its sides numbered 1 through 6 is rolled twice, first land
[#permalink]
09 Jul 2021, 08:37
09 Jul 2021, 08:37
Expert Reply
1
Bookmarks
00:00
Question Stats:
36% (01:30) correct
63% (02:37) wrong based on 22 sessions
Hide Show timer Statistics
A cube with its sides numbered 1 through 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 through 6, what is the probability that a + b is prime?
(A) 0
(B) 1/12
(C) 5/12
(D) 7/18
(E) 4/9
(A) 0
(B) 1/12
(C) 5/12
(D) 7/18
(E) 4/9
A cube with its sides numbered 1 through 6 is rolled twice, first land
[#permalink]
10 Jul 2021, 03:50
10 Jul 2021, 03:50
1
Solution:
The total number of possibilities will be 6 x 6=36.
And out of this 36 number only 2(1+1) and 12(6+6) can be computed in 1 ways rest all others can be computed in different ways.
Thus, the range of the numbers also lie between 2-12.
Prime numbers between 2-12= 2, 3, 5, 7, 11
2 can be formed in 1 way= 1+1=2
3 can be formed in 2 ways= 1+2 & 2+1
5 can be formed in 4 ways= 1+4, 4+1, 2+3, 3+2
7 can be formed in 6 ways= 1+6, 6+1, 2+5, 5+2, 3+4, & 4+3
11 can be formed in 2 ways= 6+5 & 5+6
Therefore the above sums up to 15 possible ways
Probability that a + b is prime= \(\frac{Total number of ways the sum is prime}{ Total number of all possibilities}\)=
=\(\frac{15}{36}\)=\(\frac{5}{12}\)
IMO C
Hope this helps!
The total number of possibilities will be 6 x 6=36.
And out of this 36 number only 2(1+1) and 12(6+6) can be computed in 1 ways rest all others can be computed in different ways.
Thus, the range of the numbers also lie between 2-12.
Prime numbers between 2-12= 2, 3, 5, 7, 11
2 can be formed in 1 way= 1+1=2
3 can be formed in 2 ways= 1+2 & 2+1
5 can be formed in 4 ways= 1+4, 4+1, 2+3, 3+2
7 can be formed in 6 ways= 1+6, 6+1, 2+5, 5+2, 3+4, & 4+3
11 can be formed in 2 ways= 6+5 & 5+6
Therefore the above sums up to 15 possible ways
Probability that a + b is prime= \(\frac{Total number of ways the sum is prime}{ Total number of all possibilities}\)=
=\(\frac{15}{36}\)=\(\frac{5}{12}\)
IMO C
Hope this helps!
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1111
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Re: A cube with its sides numbered 1 through 6 is rolled twice, first land
[#permalink]
15 Oct 2022, 22:12
15 Oct 2022, 22:12
Given that A cube with its sides numbered 1 through 6 is rolled twice, first landing on a and then landing on b. and We need to find If any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6, what is the probability that a + b is prime?
As we are rolling the cube twice => Number of cases = \(6^2\) = 36
First roll gives a and second roll gives b and we need to find the Probability that a+b is prime => Sum of the two rolls is prime
We know that out of the numbers from 2(1+1) to 12 (6+6) we have only five prime numbers and they are 2, 3, 5, 7 and 11
(Watch this video if you are not aware of Prime Numbers)
Following are the possible cases in which sum of the two rolls is a prime number
(1,1), (1,2), (1,4), (1,6)
(2,1), (2,3), (2,5)
(3,2), (3,4)
(4,1), (4,3)
(5,2), (5,6)
(6,1), (6,5)
=> 15 possibilities
=> Probability that a + b is prime = \(\frac{15}{36}\) = \(\frac{5}{12}\)
So, Answer will be C
Hope it helps!
Watch the following video to learn How to Solve Dice Rolling Probability Problems
As we are rolling the cube twice => Number of cases = \(6^2\) = 36
First roll gives a and second roll gives b and we need to find the Probability that a+b is prime => Sum of the two rolls is prime
We know that out of the numbers from 2(1+1) to 12 (6+6) we have only five prime numbers and they are 2, 3, 5, 7 and 11
(Watch this video if you are not aware of Prime Numbers)
Following are the possible cases in which sum of the two rolls is a prime number
(1,1), (1,2), (1,4), (1,6)
(2,1), (2,3), (2,5)
(3,2), (3,4)
(4,1), (4,3)
(5,2), (5,6)
(6,1), (6,5)
=> 15 possibilities
=> Probability that a + b is prime = \(\frac{15}{36}\) = \(\frac{5}{12}\)
So, Answer will be C
Hope it helps!
Watch the following video to learn How to Solve Dice Rolling Probability Problems
