• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Peter rolls two dice at the same time. What is . . . tagged by: M7MBA ##### This topic has 4 expert replies and 0 member replies ## Peter rolls two dice at the same time. What is . . . Peter rolls two dice at the same time. What is the probability that he will roll a double? a) 1/12 b) 1/36 c) 1/6 d) 5/12 e) 1/3 The OA is C. I got confused here. I thought it should be B. Experts, may you explain this PS question to me? Thanks. ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 M7MBA wrote: Peter rolls two dice at the same time. What is the probability that he will roll a double? a) 1/12 b) 1/36 c) 1/6 d) 5/12 e) 1/3 The OA is C. I got confused here. I thought it should be B. Experts, may you explain this PS question to me? Thanks. You found the probability that Peter would roll two of one particular number. If, for example, we wanted the probability that Peter rolled two 1's, you'd have been right. But he could have rolled two 2's or two 3's, etc. Put another way, the total number of possible outcomes is 6*6 = 36. The total number of ways to roll two of the same number would be 6. (two 1's, two 2's, two 3's, two 4's, two 5's, or two 6's.) Probability of rolling two of the same number = 6/36 = 1/6. The answer is C _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

### GMAT/MBA Expert

Elite Legendary Member
Joined
23 Jun 2013
Posted:
10197 messages
Followed by:
496 members
2867
GMAT Score:
800
Hi M7MBA,

When the possible outcomes are limited, you might find it beneficial to 'write everything out' - while it would take a little bit of work, you would be able to physically see everything, which would make dealing with the concept easier.

Since we are rolling two 6-sided dice, there are (6)(6) = 36 possible outcomes. Those outcomes are....

11,12,13,14,15,16
21,22,23,24,25,26
31,32,33,34,35,36
41,42,43,44,45,46
51,52,53,54,55,56
61,62,63,65,65,66

There are 6 'pairs' of numbers (11, 22, 33, 44, 55, 66), so the answer to the question is 6/36 = 1/6

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

### GMAT/MBA Expert

GMAT Instructor
Joined
04 Oct 2017
Posted:
551 messages
Followed by:
11 members
180
Quote:
Peter rolls two dice at the same time. What is the probability that he will roll a double?

a) 1/12

b) 1/36

c) 1/6

d) 5/12

e) 1/3

The OA is C.

I got confused here. I thought it should be B. Experts, may you explain this PS question to me? Thanks.
Hi M7MBA,
Let's take a look at your question.

Peter rolls two dice at a time, so let's first find the total number of outcomes.

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

All possible outcomes when two dice are rolled at the same time = 36
We are asked to find the probability that he will roll a double.

The outcomes for rolling a double will be:
(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)

Total outcomes for rolling a double = 6

Probability of rolling a double = (Total outcomes for rolling a double) / (All possible outcomes when two dice are rolled)
Probability of rolling a double = 6/36 = 1/6

Therefore, Option C is correct.

Hope it helps.
I am available, if you'd like any follow up.

_________________
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now.

### GMAT/MBA Expert

GMAT Instructor
Joined
08 Dec 2008
Posted:
12975 messages
Followed by:
1249 members
5254
GMAT Score:
770
M7MBA wrote:
Peter rolls two dice at the same time. What is the probability that he will roll a double?

a) 1/12

b) 1/36

c) 1/6

d) 5/12

e) 1/3
Notice that the probability doesn't change if we roll one die first and the other die second. So, let's do this.

Let die #1 the first die, and let die #2 be the second dice

P(both dice are the same) = P(die #1 is any value AND die #2 matches die #1)
= P(die #1 is any value) x P(die #2 matches die #1)
= 1 x 1/6
= 1/6
= C

ASIDE: Some people might wonder how I found the first probability to equal 1.
We need to recognize that the first die can be any value and, in order to get a double, the second guy must match the first die.
Once we have rolled the first die, there is a probability of 1/6 that the second die matches the first die.

Cheers,
Brent

_________________
Brent Hanneson â€“ Creator of GMATPrepNow.com
Use my video course along with

And check out all of these free resources

GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months!
• FREE GMAT Exam
Know how you'd score today for $0 Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

### Top First Responders*

1 Ian Stewart 57 first replies
2 Brent@GMATPrepNow 31 first replies
3 Jay@ManhattanReview 29 first replies
4 GMATGuruNY 21 first replies
5 ceilidh.erickson 15 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

199 posts
2 Max@Math Revolution

Math Revolution

84 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

69 posts
4 Ian Stewart

GMATiX Teacher

65 posts
5 GMATGuruNY

The Princeton Review Teacher

40 posts
See More Top Beat The GMAT Experts