Last visit was: 04 Nov 2024, 20:20 It is currently 04 Nov 2024, 20:20

Close

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

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 GRE 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.

Close

Request Expert Reply

Confirm Cancel
User avatar
Retired Moderator
Joined: 07 Jun 2014
Posts: 4813
Own Kudos [?]: 11136 [3]
Given Kudos: 0
GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
Send PM
User avatar
Retired Moderator
Joined: 07 Jun 2014
Posts: 4813
Own Kudos [?]: 11136 [0]
Given Kudos: 0
GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
Send PM
avatar
Intern
Intern
Joined: 08 Oct 2018
Posts: 5
Own Kudos [?]: 1 [0]
Given Kudos: 0
Send PM
avatar
Supreme Moderator
Joined: 01 Nov 2017
Posts: 371
Own Kudos [?]: 467 [0]
Given Kudos: 0
Send PM
Re: Three dice are rolled simultaneously. What is the [#permalink]
1
Expert Reply
sandy wrote:
Three dice are rolled simultaneously. What is the probability that exactly two of the dice will come up as the same number?

A. \(\frac{5}{12}\)
B. \(\frac{11}{24}\)
C. \(\frac{25}{54}\)
D. \(\frac{13}{27}\)
E. \(\frac{1}{2}\)

Drill 2
Question: 12
Page: 526-527



So,

Total ways = 6*6*6

WITH restrictions
Ways to choose 2 with same number out of 23 = 3C2=3 ways..
These 2 can have any of the 6 sides = 6 ways
The third can take any of the remaining 5, so 5 ways
Total = 3*5*6

Probability = \(\frac{3*5*6}{6*6*6}=\frac{5}{12}\)
avatar
Manager
Manager
Joined: 04 Feb 2019
Posts: 204
Own Kudos [?]: 418 [0]
Given Kudos: 0
Send PM
Re: Three dice are rolled simultaneously. What is the [#permalink]
Expert Reply
We can also use the complement here. The total number of possibilities is 6*6*6 = 216.

In 6 of these possibilities, all the dice are the same number. That's a probability of \(\frac{6}{216}\).

What's the probability that none of the dice come up as the same number?

Well, we have a probability of 1 that the first die will be a number. Then we have a \(\frac{5}{6}\) probability that the next die will not match it. And a \(\frac{4}{6}\) probability that the third will not match either of the previous two. Together: \(1 \times \frac{5}{6} \times \frac{4}{6} = \frac{20}{36} = \frac{120}{216}\).

So we have the probability that all the dice are the same, and that none are the same. The only other remaining possibility is that two dice are the same. So:

\(1 - \frac{6}{216} - \frac{120}{216} = \frac{90}{216} = \frac{5}{12}\)
Moderator
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1111
Own Kudos [?]: 960 [0]
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)
Send PM
Re: Three dice are rolled simultaneously. What is the [#permalink]
Given that Three dice are rolled simultaneously and We need to find What is the probability that exactly two of the dice will come up as the same number?

As we are rolling three dice => Number of cases = \(6^3\) = 216

Out of the three rolls lets find out the two rolls in which we will get the same number.
We can get that in 3C2 ways = \(\frac{3!}{2!*1!}\) = 3 ways

Now these two numbers can be any number out of 6 => First number we can pick in 6 ways and second number we can pick in 1 way as it has to be the same as the first number

For the third number we have 5 ways as it has to be different from the first two

=> Total number of ways = 3 * 6 * 1 * 5

=> Probability that exactly two of the dice will come up as the same number = \(\frac{3 * 6 * 1 * 5}{6^3}\) = \(\frac{5}{12}\)

So, Answer will be A
Hope it helps!

Watch the following video to learn How to Solve Dice Rolling Probability Problems

Prep Club for GRE Bot
Re: Three dice are rolled simultaneously. What is the [#permalink]
Moderators:
GRE Instructor
77 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
228 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne