Last visit was: 23 Apr 2026, 05:56

It is currently 23 Apr 2026, 05:56

Toolkit

Practice Tests

Quantitative Questions

Problem Solving (PS)

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

Request Expert Reply

Confirm Cancel

Apr 23
Free full-length test!
08:00 PM PDT
-
09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Apr 23
A Non-Native’s Journey to GMAT 695 with V88 (99th percentile)
01:30 AM EDT
-
02:30 AM EDT
Struggling with GMAT Verbal as a non-native speaker? Harsh improved his score from 595 to 695 in just 45 days—and scored a 99 %ile in Verbal (V88)! Learn how smart strategy, clarity, and guided prep helped him gain 100 points.
Apr 25
From ‘GMAT Is Not for Me’ to a 695— Beating Her Target by 50 Points
12:30 AM EDT
-
01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 26
Score High on the GMAT with Target Test Prep
10:00 AM EDT
-
11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 27
Try OnDemand GMAT Masterclass
11:00 AM EDT
-
12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 28
Join - GMAT Day!
08:00 AM PDT
-
11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.

Back to Forum

Create Topic

12 Days of Christmas GMAT Competition 2025 - Day 4: A pair of fair six

1 2 3 4

Bunuel

Math Expert

Joined: 02 Sep 2009

Last visit: 23 Apr 2026

Posts: 109,778

Own Kudos:

810,772

[20]

Given Kudos: 105,853

Products:

Expert

Expert reply

Posts: 109,778

Kudos: 810,772

[20]

18 Dec 2025, 09:00

Kudos

Bookmarks

00:00

Start Timer

Pause Timer

Resume Timer

Show Answer

Hide

Show

History

Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

50% (01:29) correct

50% (01:17) wrong

based on 246 sessions

History

Date

Time

Result

Not Attempted Yet

A pair of fair six-sided dice is rolled once. If at least one die shows a prime number, what is the probability that both dice show prime numbers?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 3/4

M46-12

Gift

12 Days of Christmas Competition

This question is part of our holiday event

Win $40,000 in prizes: courses, tests, and more

Show Answer

Official Answer

Most Helpful Reply

Bunuel

Math Expert

Joined: 02 Sep 2009

Last visit: 23 Apr 2026

Posts: 109,778

Own Kudos:

810,772

[2]

Given Kudos: 105,853

Products:

Expert

Expert reply

Posts: 109,778

Kudos: 810,772

[2]

18 Dec 2025, 10:00

Kudos

Bookmarks

Bunuel

A pair of fair six-sided dice is rolled one. If at least one die shows a prime number, what is the probability that both dice show prime numbers?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 3/4

GMAT Club Official Explanation:

Prime faces: 2, 3, 5
Non-prime faces: 1, 4, 6

Total number of outcomes = 6 * 6 = 36.

We want only the outcomes in which at least one die shows a prime. The only outcomes that do not satisfy this are those where both dice are non-prime. Each die has 3 non-prime faces, so the number of outcomes with no prime at all is 3 * 3 = 9.

So the number of outcomes with at least one prime is 36 - 9 = 27.

The number of outcomes where both dice show primes is 3 * 3 = 9, since each die has 3 prime faces.
We are told that at least one die shows a prime, so we look only at those 27 outcomes. Among these, 9 have both dice prime, so the required probability is 9/27 = 1/3.

Answer: B.

General Discussion

ghimires28

Joined: 19 Jul 2025

Last visit: 23 Apr 2026

Posts: 27

Own Kudos:

[1]

Given Kudos: 1

Location: Nepal

Concentration: Technology, Entrepreneurship

Posts: 27

Kudos: 18

[1]

18 Dec 2025, 09:12

Kudos

Bookmarks

In this question it is given that the first dice show a prime number is sure given so that probability is 1 for the second dice the probability is 1/2{2,3,5}.
1*1/2=1/2

Archit3110

Major Poster

Joined: 18 Aug 2017

Last visit: 23 Apr 2026

Posts: 8,628

Own Kudos:

5,190

[1]

Given Kudos: 243

Status:You learn more from failure than from success.

Location: India

Concentration: Sustainability, Marketing

GMAT Focus 1: 545 Q79 V79 DI73 Verified score

GMAT Focus 2: 645 Q83 V82 DI81 Verified score

GPA: 4

WE:Marketing (Energy)

Products:

GMAT Focus 2: 645 Q83 V82 DI81 Verified score

Posts: 8,628

Kudos: 5,190

[1]

18 Dec 2025, 09:12

Kudos

Bookmarks

A pair of fair six-sided dice is rolled once. If at least one die shows a prime number, what is the probability that both dice show prime numbers?
A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 3/4

prime in dice (2,3,5)
P of getting prime 1/2
in both dice it will be 1/2 * 1/2 = 1/4
P of getting a prime and a non prime in dice role
3*3 = 9
possible outcomes in two dice roles are 6*6 = 26
9/36 ; 1/4
P of getting at least a prime number 1-1/4 = 3/4

P of both show prime with atleast one shows prime 1/4 / 3/4 = 1/3
OPTION B ;1/3 is correct

paragw

Joined: 17 May 2024

Last visit: 22 Apr 2026

Posts: 189

Own Kudos:

193

[1]

Given Kudos: 38

Posts: 189

Kudos: 193

[1]

18 Dec 2025, 09:12

Kudos

Bookmarks

Prime faces are 2,3, and 5, so probability a die shows a prime is 1/2.

Probability both dice show primes = 1/2 * 1/2 = 1/4
Probability at least one die shows a prime = 1 - 1/4 = 3/4

Required probability
=> (1/4 )/(3/4)
=> 1/3

Answer: B

Abhiswarup

Joined: 07 Apr 2024

Last visit: 12 Jan 2026

Posts: 198

Own Kudos:

172

[1]

Given Kudos: 42

Location: India

Posts: 198

Kudos: 172

[1]

18 Dec 2025, 09:18

Kudos

Bookmarks

Dice 1 & Dice 2 can show nos 1,2,3,4,5,6, Prime Nos= 2,3,5 Non prime nos=1,4,6
Total possibilities= 6*6=36
Total possibilities wherein both nos as prime= 3*3=9
Total possibilities wherein both nos are non prime= 3*3=9
Total possibilities wherein at least one no. is prime= Total possibilities-Total possibilities wherein both nos are not prime= 36-9=27
P(both prime/at least one prime)=9/27=1/3
Answer is B

Kinshook

Major Poster

Joined: 03 Jun 2019

Last visit: 23 Apr 2026

Posts: 5,986

Own Kudos:

5,858

[1]

Given Kudos: 163

Location: India

Schools: HBS '26 CBS '26 Wharton '26

GMAT 1: 690 Q50 V34 Verified score

WE:Engineering (Transportation)

Products:

Schools: HBS '26 CBS '26 Wharton '26

GMAT 1: 690 Q50 V34 Verified score

Posts: 5,986

Kudos: 5,858

[1]

18 Dec 2025, 09:18

Kudos

Bookmarks

Numbers on dice = {1,2,3,4,5,6}
Prime numbers on dice = {2,3,5}
Non-prime numbers on dice = {1,4,6}

A pair of dice is rolled once.
Total number of way both dice show numbers = 6*6 = 36
Number of ways both dice show non-prime numbers = 3*3 = 9
Number of ways at least one dice shows a prime number = 36 - 9 = 27
Number of ways both dice show prime numbers = 3*3 = 9

If at least once dice shows a prime number, the probability that both dice show prime numbers = 9/27 = 1/3

IMO B

Chaithanya20

Joined: 15 Dec 2025

Last visit: 26 Dec 2025

Posts: 14

Own Kudos:

[1]

Given Kudos: 1

Posts: 14

Kudos: 12

[1]

18 Dec 2025, 09:22

Kudos

Bookmarks

Total possible pairs = 36
No. of primes = 3
Outcomes with no primes = 3*3 = 9
Outcomes with atleast one prime = 27
Outcomes with both prime = 9
Therefore, Probability = 9/27 = 1/3

Ayeka

Joined: 26 May 2024

Last visit: 22 Apr 2026

Posts: 528

Own Kudos:

402

[1]

Given Kudos: 158

Location: India

Schools: ISB

GMAT Focus 1: 645 Q82 V83 DI80 Verified score

GPA: 4.2

Schools: ISB

GMAT Focus 1: 645 Q82 V83 DI80 Verified score

Posts: 528

Kudos: 402

[1]

18 Dec 2025, 09:24

Kudos

Bookmarks

Prime numbers on a die are 2,3,5
Toatl possible outcomes when 2 die are rolled =6*6=36
Non prime numbers on a die are 1,4,6
Total non prime outcomes =3*3=9
So, outcome where atleast one die shows a prime =36-9=27
Outcomes where both dice show prime number = 3*3=9
Probability where both dice show prime numbers =9/27=(1/3)

B

sitrem

Joined: 19 Nov 2025

Last visit: 24 Feb 2026

Posts: 91

Own Kudos:

[1]

Given Kudos: 238

Posts: 91

Kudos: 84

[1]

18 Dec 2025, 09:29

Kudos

Bookmarks

Prime numbers from 1 to 6 are 2,3,5 -> P(prime) = 3/6 = 1/2

let's call events "both prime" = X
"at least one prime" = Y

We use conditional probability formula P(X|Y) = P(X and Y) / P(Y)
P(X and Y) = P(X) since X is a subset of the event Y (if both are prime then one must be prime)
P(X|Y) = P(X) / P(Y)

P(X) = 1/2 * 1/2 = 1/4
(the two outcomes constitute independent events)
P(Y) = 1 - P("neither is prime") = 1 - (1/2 * 1/2) = 3/4

P(X|Y) = (1/4) / (3/4) = 1/3

Jxmes

Joined: 26 Jul 2018

Last visit: 22 Apr 2026

Posts: 17

Own Kudos:

Given Kudos: 12

Posts: 17

Kudos: 3

18 Dec 2025, 09:29

Kudos

Bookmarks

if this were not a conditional probability question, the answer would be 1/4

but it is, so the answer is 1/3, because we're restricted to P-P, NP-P, and P-NP.

note: each discrete outcome has the same probability because there are as many primes as non-primes Prob(prime) = Prob(non-prime) = 1/2. so you don't even need to calculate the probabilities of the individual outcomes. you can just use the outcomes themselves.

ManifestDreamMBA

Joined: 17 Sep 2024

Last visit: 21 Feb 2026

Posts: 1,387

Own Kudos:

897

[1]

Given Kudos: 243

Posts: 1,387

Kudos: 897

[1]

18 Dec 2025, 09:29

Kudos

Bookmarks

P(Atleast one dice show prime) = 1-P(no prime on either)

Prime numbers on each dice = 3 (2,3 and 5)
P(prime) = 3/6 = 1/2
P(prime on both) = 1/2 * 1/2 = 1/4

P(not prime) = 1-1/2 = 1/2
P(no prime on either) = 1/2 * 1/2 = 1/4

P(Atleast one dice show prime) = 1-1/4 =3/4

P(prime on both)/ P(atleast one dice show prime) = 1/4 / 3/4 = 1/3

answer B

Bunuel

A pair of fair six-sided dice is rolled once. If at least one die shows a prime number, what is the probability that both dice show prime numbers?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 3/4

Gift

12 Days of Christmas Competition

This question is part of our holiday event

Win $40,000 in prizes: courses, tests, and more

Sumimasen

Joined: 21 Jan 2024

Last visit: 22 Apr 2026

Posts: 36

Own Kudos:

[1]

Given Kudos: 11

Products:

Posts: 36

Kudos: 33

[1]

18 Dec 2025, 09:29

Kudos

Bookmarks

Total outcomes on a fair sided dice rolled once is 6. {any one of 1,2,3,4,5,6}
Prime = {2,3,5}. Probability of Prime outcome will be 3/6 = 1/2
Non-Prime = {1,4,6}. Probability of non-prime outcomes will also be 3/6 = 1/2.

Here, we have two dices rolled together. Condition (A) given at least one dice has prime number.
Possible scenarios of condition A = (first dice has prime and second dice has non-prime) or (first dice has non-prime and second dice has prime number) or Both dices have prime numbers.
p(A) = (1/2 x 1/2) + (1/2 x 1/2) + (1/2 x 1/2) = 3/4
With condition A, probability that both dice shows prime number will be ->
(1/2 x 1/2)/(3/4) = (1/4)/(3/4) = 1/3

Xdsa

Joined: 07 Jul 2025

Last visit: 23 Apr 2026

Posts: 57

Own Kudos:

[1]

Given Kudos: 1

Posts: 57

Kudos: 45

[1]

18 Dec 2025, 09:36

Kudos

Bookmarks

answer is 1/3

reason:

both die show prime nos is 9
no of possibility is 6x6=36
both die showing non prime nos is 9
total possibility is 36-9=9=27
probability=9/27=1/3

batman10bigman

Joined: 23 Apr 2025

Last visit: 23 Apr 2026

Posts: 44

Own Kudos:

[1]

Given Kudos: 11

Products:

Posts: 44

Kudos: 38

[1]

18 Dec 2025, 09:39

Kudos

Bookmarks

Bunuel

A pair of fair six-sided dice is rolled once. If at least one die shows a prime number, what is the probability that both dice show prime numbers?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 3/4

Gift

12 Days of Christmas Competition

This question is part of our holiday event

Win $40,000 in prizes: courses, tests, and more

The prime numbers are (2,3,5) and non prime are (1,4,6).
The total outcomes when two dice are rolled are 6x6 = 36

Atleast one prime = 1 - no primes

In cases where both are non-prime, we have to choose from numbers (1,4,6) for both dice
so we have 3x3 = 9 outcomes

Atleast one prime = 1 - 9/36
=27/36
= 1/3
= Answer choice B

Gmat860sanskar

Joined: 05 May 2023

Last visit: 23 Apr 2026

Posts: 212

Own Kudos:

113

[1]

Given Kudos: 79

Schools: ISB '26

GMAT Focus 1: 605 Q82 V78 DI80 Verified score

Products:

Schools: ISB '26

GMAT Focus 1: 605 Q82 V78 DI80 Verified score

Posts: 212

Kudos: 113

[1]

18 Dec 2025, 09:44

Kudos

Bookmarks

Bunuel

A pair of fair six-sided dice is rolled once. If at least one die shows a prime number, what is the probability that both dice show prime numbers?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 3/4

Gift

12 Days of Christmas Competition

This question is part of our holiday event

Win $40,000 in prizes: courses, tests, and more

Prime numbers in dice are 2,3,5

so probability for both dice showing prime is

1/2 * 1/2 = 1/4

Now let's see the probability for at least one prime

No prime probability is = 1/2* 1/2 = 1/4

So 1-1/4 = 3/4 is the probability for at least one dice showing a prime number

so 1/4 (both prime) divided by 3/4 (at least one prime) = 1/3

Option B is correct

yuvrajbhama

Joined: 30 Jul 2025

Last visit: 05 Apr 2026

Posts: 36

Own Kudos:

Given Kudos: 3

Location: India

Concentration: General Management, Nonprofit

Schools: Booth (Chicago) ESADE HEC MiM '26 Duke Fuqua ESSEC MiM '26

GPA: 6.6

WE:General Management (Energy)

Schools: Booth (Chicago) ESADE HEC MiM '26 Duke Fuqua ESSEC MiM '26

Posts: 36

Kudos: 20

18 Dec 2025, 09:51

Kudos

Bookmarks

TOTAL NUMBER OF FAVOURABLE OUT COME IF 1,2,3,5ON DICE A AND MULTIPLIED BY ON DICE =4*4= 16
AND TOTAL OUTCOME ARE 1,2,3,5 IS FIXED ON ONE DICE AND OTHER HAS 6 SO 4*6=24

PROBABILTIY IS = TO FAVOURABLE OUTCOME / TOTAL OUTCOME
16/24= 2/3

Bunuel

A pair of fair six-sided dice is rolled once. If at least one die shows a prime number, what is the probability that both dice show prime numbers?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 3/4

Gift

12 Days of Christmas Competition

This question is part of our holiday event

Win $40,000 in prizes: courses, tests, and more

vikramadityaa

Joined: 28 Jul 2025

Last visit: 23 Dec 2025

Posts: 55

Own Kudos:

[1]

Given Kudos: 1

Posts: 55

Kudos: 41

[1]

18 Dec 2025, 09:51

Kudos

Bookmarks

Bunuel

A pair of fair six-sided dice is rolled once. If at least one die shows a prime number, what is the probability that both dice show prime numbers?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 3/4

Gift

12 Days of Christmas Competition

This question is part of our holiday event

Win $40,000 in prizes: courses, tests, and more

Let P='a die shows a prime number.'
P(prime)=(3/6)=(1/2)
Probability both dice are prime: (1/2)*(1/2)=(1/4)
"At least one prime"=1-"no primes"
P(no prime)=(3/6)=(1/2)
Probability both dice are non prime: (1/2)*(1/2)=(1/4)
P(at least one prime)=1-(1/4)=3/4
P(both prime|at least one prime)=(1/4)/(3/4)=1/3 (Option B)

Hence, Option B.

Rahilgaur

Joined: 24 Jun 2024

Last visit: 26 Jan 2026

Posts: 162

Own Kudos:

125

[1]

Given Kudos: 47

GMAT Focus 1: 575 Q81 V82 DI72 Verified score

Products:

GMAT Focus 1: 575 Q81 V82 DI72 Verified score

Posts: 162

Kudos: 125

[1]

18 Dec 2025, 09:56

Kudos

Bookmarks

Bunuel

A pair of fair six-sided dice is rolled once. If at least one die shows a prime number, what is the probability that both dice show prime numbers?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 3/4

Gift

12 Days of Christmas Competition

This question is part of our holiday event

Win $40,000 in prizes: courses, tests, and more

No. of Pair with at least one prime number => (1,2) (1,3)(1,5) ..(2,1)(2,2) (2,3)(2,4) (2,5)(2,6)...(3,1) (3,2) (3,3)(3,4) (3,5)(3,6) ..(4,2) (4,3)(4,5)..(5,1)(5,2)(5,3)(5,4) (5,5)(5,6)..(6,1)(6,2) (6,3) (6,5) = 27

No, of pair where by both show prime numbers -> (2,2) (2,3) (2,5)... (3,2) ( 3,3) (3,5).. (5,2) (5,3) (5,5) = 9

Probability = 9/27 = 1/3 B Answer

prepapr

Joined: 06 Jan 2025

Last visit: 22 Apr 2026

Posts: 92

Own Kudos:

[1]

Given Kudos: 5

GMAT Focus 1: 615 Q85 V80 DI77 Verified score

Posts: 92

Kudos: 82

[1]

18 Dec 2025, 10:08

Kudos

Bookmarks

Prime numbers on a die - 2 3 5
Number of prime numbers in a die = 3
Probability of getting a prime number when rolled once is 1/2
Probability that atleast one die shows a prime number = 1 - probability that none of the dice shows up prime numbers
= 1 - (1/2)*(1/2)
= 1 - 1/4 = 3/4
Probability that both dice show prime numbers = (1/2)*(1/2) = 1/4
Conditional probability given that atleast one die shows a prime number, probability of getting prime numbers on both dice = (1/4)/(3/4) = 1/3

Bunuel

A pair of fair six-sided dice is rolled once. If at least one die shows a prime number, what is the probability that both dice show prime numbers?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 3/4

Gift

12 Days of Christmas Competition

This question is part of our holiday event

Win $40,000 in prizes: courses, tests, and more