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

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: PS dice probability [#permalink]
16 Nov 2007, 11:19

2

This post received KUDOS

young_gun wrote:

Two fair dices are rolled. Find the probability that the number showing on the first die is less than the number showing on the second die.

5/12. Here are two approaches:

a) Count up the possibilities. If the first die is 1, there are 5 greater numbers on the second: 1/6 * 5/6 = 5/36. If the first die is 2, there are 4: 1/6 * 4/6 = 4/36. Etc. The result:

5/36 + 4/ 36 + 3/36 + 2/36 + 1/36 = 15/36 = 5/12.

b) You can assume that, as long as the dice don't show matching numbers, there's an even chance that either the first or the second is greater. So the probability that the first is less is 1/2 the probability that the dice don't match.

There's a 1/6 chance that the dice do match. So the probability of non-matching is 5/6, and the probability that the first is less than the second is 5/12.

Re: PS dice probability [#permalink]
16 Nov 2007, 13:12

johnrb wrote:

young_gun wrote:

Two fair dices are rolled. Find the probability that the number showing on the first die is less than the number showing on the second die.

5/12. Here are two approaches:

a) Count up the possibilities. If the first die is 1, there are 5 greater numbers on the second: 1/6 * 5/6 = 5/36. If the first die is 2, there are 4: 1/6 * 4/6 = 4/36. Etc. The result:

5/36 + 4/ 36 + 3/36 + 2/36 + 1/36 = 15/36 = 5/12.

b) You can assume that, as long as the dice don't show matching numbers, there's an even chance that either the first or the second is greater. So the probability that the first is less is 1/2 the probability that the dice don't match.

There's a 1/6 chance that the dice do match. So the probability of non-matching is 5/6, and the probability that the first is less than the second is 5/12.

Re: PS dice probability [#permalink]
28 Sep 2009, 03:20

2

This post received KUDOS

Two fair dices are rolled. Find the probability that the number showing on the first die is less than the number showing on the second die.

Soln: Total number of outcomes is = 6 * 6 = 36 ways

The number of outcomes in which number on first die is less than that on the second is {1,2},{1,3},{1,4},{1,5},{1,6} {2,3},{2,4},{2,5},{2,6} {3,4},{3,5},{3,6} {4,5},{4,6} {5,6} Totally 15 ways

Re: PS dice probability [#permalink]
28 Sep 2009, 03:29

johnrb wrote:

b) You can assume that, as long as the dice don't show matching numbers, there's an even chance that either the first or the second is greater. So the probability that the first is less is 1/2 the probability that the dice don't match.

There's a 1/6 chance that the dice do match. So the probability of non-matching is 5/6, and the probability that the first is less than the second is 5/12.

Re: PS dice probability [#permalink]
02 May 2011, 22:10

1

This post received KUDOS

total cases = 36 6 cases are when (1,1),(2,2) and so on. hence cases there numbers are different = 36-6 = 30 half of these cases are when dice 1 > dice 2 =15.

hence probability = 15/36 = 5/12 _________________

Re: Two fair dices are rolled. Find the probability that the [#permalink]
26 Jan 2013, 04:19

2

This post received KUDOS

Expert's post

manimgoindowndown wrote:

how's there a 1/6 chance that both die match?

There are total of 6*6=36 cases, out of which in 6 cases the numbers on both dies are the same: (1, 1), (2, 2), (3, 3), (4, 4), (5, 5) and (6, 6). So, the probability that we'll get the same number on both dies is 6/36=1/6.

Complete solution: Two fair dices are rolled. Find the probability that the number showing on the first die is less than the number showing on the second die.

Total ways = 6*6=36;

Ties in 6 ways;

There are 36-6=30 cases left, in half of them the number on the first die will be more than the number on the second die and in other half of the cases the number on the first die will be less than the number on the second die.

Hence, the probability that the number showing on the first die is less than the number showing on the second die is 15/36=5/12.

Re: Two fair dices are rolled. Find the probability that the [#permalink]
29 May 2014, 05:44

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: Two fair dices are rolled. Find the probability that the [#permalink]
16 Jun 2015, 02:22

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Interested in applying for an MBA? In the fourth and final part of our live QA series with guest expert Chioma Isiadinso, co-founder of consultancy Expartus and former admissions...