NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 03:16 It is currently 24 Apr 2024, 03:16
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT 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 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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

What is the probability of rolling two fair dice and having both dice

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92901
Own Kudos [?]: 618693 [6]
Given Kudos: 81586
Send PM
CAT Tests Forum Quiz Mode
What is the probability of rolling two fair dice and having both dice [#permalink] New post   29 Mar 2017, 04:53
6
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

78% (01:02) correct 22% (01:14) wrong based on 210 sessions
Hide Show timer Statistics
What is the probability of rolling two fair dice and having both dice show distinct odd numbers?

A. 1/36
B. 1/12
C. 1/6
D. 1/2
E. 35/36
ShowHide Answer
Official Answer
C
User avatar
S
mohshu
Senior Manager
Senior Manager
Joined: 21 Mar 2016
Posts: 448
Own Kudos [?]: 117 [3]
Given Kudos: 103
Send PM
Reviews Badge
Re: What is the probability of rolling two fair dice and having both dice [#permalink] New post   29 Mar 2017, 08:45
2
Kudos
1
Bookmarks
odd numbers = 1,3,5

two dice will give 3 x 3 = 9 combination of odd nos... but
combination of 2 same odd nos = (1,1) (3,3) (5,5)

hence 9-3 =6

prob = 6/36 = 1/6

ans 1/6
avatar
B
matthewsmith_89
Manager
Manager
Joined: 06 Dec 2016
Posts: 196
Own Kudos [?]: 57 [1]
Given Kudos: 10
Send PM
Re: What is the probability of rolling two fair dice and having both dice [#permalink] New post   30 Mar 2017, 11:16
1
Kudos
(1,3), (1,5), (3,5), (3,1), (5,1), (5,3)

6 x 6 = 36

6/36 = 1/6 which is answer C
User avatar
P
Hatakekakashi
VP
VP
Joined: 07 Jan 2016
Posts: 1250
Own Kudos [?]: 464 [0]
Given Kudos: 126
Location: United States (MO)
GMAT 1: 710 Q49 V36
Send PM
Reviews Badge
Re: What is the probability of rolling two fair dice and having both dice [#permalink] New post   30 Mar 2017, 13:00
total possible 1 3 5 (3) and 1 3 5 (3) = 9

cases excluded - 11 33 55

9-3 = 6

6/36

C
avatar
B
ar500
Intern
Intern
Joined: 29 Apr 2015
Posts: 16
Own Kudos [?]: 9 [1]
Given Kudos: 4
GPA: 3.89
Send PM
Re: What is the probability of rolling two fair dice and having both dice [#permalink] New post   30 Mar 2017, 16:49
1
Kudos
With the regard to the popular 1/6 answer, do you guys think it is problematic that you are counting both "1,3" and "3,1" as part of your 6 positive outcomes? Does sequence matter in a dice roll?
User avatar
P
Hatakekakashi
VP
VP
Joined: 07 Jan 2016
Posts: 1250
Own Kudos [?]: 464 [0]
Given Kudos: 126
Location: United States (MO)
GMAT 1: 710 Q49 V36
Send PM
Reviews Badge
Re: What is the probability of rolling two fair dice and having both dice [#permalink] New post   30 Mar 2017, 22:58
ar500 wrote:
With the regard to the popular 1/6 answer, do you guys think it is problematic that you are counting both "1,3" and "3,1" as part of your 6 positive outcomes? Does sequence matter in a dice roll?



IMO , yes sequence matters

1st throw having a 1 on the dice can lead to six options on the second dice.

Assume this situation

In a Football (soccer) match , the final score is 3-1
now first player X of a team scores a hattrick , then in the dying minutes of the game , a player from the opposition scores a goal and makes it 3-1
now this score can be achieved in multiple ways and we notice that each way is different

I'm not the best person around here to explain it in a lucid way but i hope you got my point


Regards,
HK
avatar
B
malevg
Intern
Intern
Joined: 15 Jun 2013
Posts: 33
Own Kudos [?]: 17 [0]
Given Kudos: 33
Schools: Ivey '19 (I)
GMAT 1: 690 Q49 V35
GPA: 3.82
Send PM
Re: What is the probability of rolling two fair dice and having both dice [#permalink] New post   30 Mar 2017, 23:38
The probability of one dice having odd side is 3/6=1/2. The same thing with the second dice. The probability of the second dice having distinct number is 2/3 (we have 3 possible numbers but only 2 that satisfy "distinct" condition).
Therefore general probability equals 1/2*1/2*2/3=1/6.
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14816
Own Kudos [?]: 64889 [3]
Given Kudos: 426
Location: Pune, India
Send PM
Re: What is the probability of rolling two fair dice and having both dice [#permalink] New post   31 Mar 2017, 03:27
2
Kudos
1
Bookmarks
Expert Reply
ar500 wrote:
With the regard to the popular 1/6 answer, do you guys think it is problematic that you are counting both "1,3" and "3,1" as part of your 6 positive outcomes? Does sequence matter in a dice roll?


Since the problem doesn't say that the dice are identical, think about them as two different coloured dice - one red and one yellow.
A 1 on the red die and 3 on the yellow die is different from a 3 on the red die and 1 on the yellow die.

So, there are 3 ways of getting an odd outcome on the red die and 2 ways of getting an odd outcome on the yellow die. In all there are 3*2 = 6 ways of satisfying the condition.

Of course, total cases are 6*6 = 36

Probability = 6/36 = 1/6
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18753
Own Kudos [?]: 22043 [3]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: What is the probability of rolling two fair dice and having both dice [#permalink] New post   31 Mar 2017, 12:42
2
Kudos
1
Bookmarks
Expert Reply
Bunuel wrote:
What is the probability of rolling two fair dice and having both dice show distinct odd numbers?

A. 1/36
B. 1/12
C. 1/6
D. 1/2
E. 35/36


We need to determine the probability that the two dice show distinct odd numbers.

Let’s start with die #1: There are 3 odd numbers, and thus the probability of rolling an odd number is 3/6 = 1/2. When rolling die #2, since we must roll a different odd number, the probability of doing so is 2/6 = 1/3.

Thus, the probability is 1/2 x 1/3 = 1/6.

Answer: C
User avatar
L
EgmatQuantExpert
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3726
Own Kudos [?]: 16832 [0]
Given Kudos: 165
Send PM
What is the probability of rolling two fair dice and having both dice [#permalink] New post   31 Mar 2017, 13:55
Expert Reply
Bunuel wrote:
What is the probability of rolling two fair dice and having both dice show distinct odd numbers?

A. 1/36
B. 1/12
C. 1/6
D. 1/2
E. 35/36


Solution



    • Odd numbers on a die are (\(1,3\) or \(5\))

    • We need distinct odd numbers on the two dice.

      o Thus, the first die can show any one of the 3 odd numbers, which is \(= {}^3C_1\)

      o The second die can then show the other 2 odd numbers, which is \(= {}^2C_1\)

      o Thus, favorable cases of two dice showing distinct odd numbers \(= 3 * 2 = 6\)


    • Total number of cases are \(6*6 = 36\)

    • Thus, Probability \(= \frac{6}{36} = \frac{1}{6}\)

    • Correct Answer is Option C.

Thanks,
Saquib
Quant Expert
e-GMAT

Aiming to score Q50 or higher in GMAT Quant? Attend this webinar on 2nd April to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes. Register

avatar
B
FB2017
Manager
Manager
Joined: 18 Jun 2017
Posts: 50
Own Kudos [?]: 13 [0]
Given Kudos: 165
Send PM
Re: What is the probability of rolling two fair dice and having both dice [#permalink] New post   03 Aug 2017, 01:35
Distinct odd values from dice 1 can have 3 outcomes.
Similarly from dice 2.
Total 6 favorable outcomes from 2 dices.
Total outcomes =36
Probability of favorable outcomes=6/36=1/6
Option C.
avatar
B
pankajpatwari
Intern
Intern
Joined: 17 Aug 2018
Posts: 17
Own Kudos [?]: 1 [0]
Given Kudos: 22
Send PM
Re: What is the probability of rolling two fair dice and having both dice [#permalink] New post   13 Aug 2019, 19:48
EgmatQuantExpert wrote:
Bunuel wrote:
What is the probability of rolling two fair dice and having both dice show distinct odd numbers?

A. 1/36
B. 1/12
C. 1/6
D. 1/2
E. 35/36


Solution



    • Odd numbers on a die are (\(1,3\) or \(5\))

    • We need distinct odd numbers on the two dice.

      o Thus, the first die can show any one of the 3 odd numbers, which is \(= {}^3C_1\)


      o The second die can then show the other 2 odd numbers, which is \(= {}^2C_1\)

      o Thus, favorable cases of two dice showing distinct odd numbers \(= 3 * 2 = 6\)


    • Total number of cases are \(6*6 = 36\)

    • Thus, Probability \(= \frac{6}{36} = \frac{1}{6}\)

    • Correct Answer is Option C.

Thanks,
Saquib
Quant Expert
e-GMAT

Aiming to score Q50 or higher in GMAT Quant? Attend this webinar on 2nd April to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes. Register



Hi E-GMAT Team,
I request reference to your "Must Read Articles & Practice Questions to score 51". In the probability section one of the key takeaways you have emphasized upon is: "If there are more than one arrangements possible then we will find the probability of only one case and multiply it by the total number of possible arrangements".

By that logic, no. of possible arrangements in the question under discussion are 6:
1,3;1,5;3,5;3,1;5,1;5,3

So shudn't the probability be be then:

6*3/6*2/6=1

I know i am not understanding it right. but cud u plzz guide me where??
User avatar
D
BrushMyQuant
Tutor
Joined: 05 Apr 2011
Status:Tutor - BrushMyQuant
Posts: 1777
Own Kudos [?]: 2094 [0]
Given Kudos: 100
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Send PM
Re: What is the probability of rolling two fair dice and having both dice [#permalink] New post   08 Oct 2022, 10:17
Expert Reply
Top Contributor
We need to find What is the probability of rolling two fair dice and having both dice show distinct odd numbers?

As we are rolling two dice => Number of cases = \(6^2\) = 36

Now we have three odd numbers in 1 to 6 -> 1, 3, 5. Lets start writing the possible cases where two dice will show distinct odd numbers

- If we get 1 in the first roll then the second roll can give us other two odd numbers which are 3 and 5
=> (1,3), (1,5) => 2 cases

Similarly, we will get following cases
(3,1), (3,5)
(5,1), (5,3)

=> 6 cases

=> Probability that rolling two fair dice and having both dice show distinct odd numbers = \(\frac{6}{36}\) = \(\frac{1}{6}\)

So, Answer will be C
Hope it helps!

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

User avatar
S
Nikkz99
Intern
Intern
Joined: 23 Jun 2021
Posts: 47
Own Kudos [?]: 29 [0]
Given Kudos: 230
Location: India
GPA: 3.54
Send PM
Forum Quiz Mode
Re: What is the probability of rolling two fair dice and having both dice [#permalink] New post   13 Sep 2023, 02:27
Simpler way to solve this question is,
No : of odd faces in a dice -> {1,3,5} therefore, 3 numbers

Question states that we there must be "2 distinct odd faces".

Therefore we mustn't get -> {(1,1), (3,3), (5,5)}

Probability of getting odd number in die 1 -> 1/2
Probability of getting Distinct Odd number in die 2 -> 2/6 => 1/3

P(Getting two distinct odd number on both the dice) = 1/2 * 1/3 = 1/6
GMAT Club Bot
gmatclubot
Re: What is the probability of rolling two fair dice and having both dice [#permalink]
13 Sep 2023, 02:27
Moderators:
Bunuel
Math Expert
92901 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions