GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Dec 2019, 22:22 ### 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

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.  # If a fair die is rolled three times, what is the probability that a 3

Author Message
TAGS:

### Hide Tags

Manager  Joined: 06 Jun 2014
Posts: 85
Location: United States
Concentration: Finance, General Management
GMAT 1: 450 Q27 V21 GPA: 3.47
If a fair die is rolled three times, what is the probability that a 3  [#permalink]

### Show Tags

3
10 00:00

Difficulty:   25% (medium)

Question Stats: 74% (01:20) correct 26% (01:28) wrong based on 269 sessions

### HideShow timer Statistics

If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?

A) 25/36

B) 125/216

C) 91/216

D) 11/36

E) 36/216
CEO  S
Joined: 20 Mar 2014
Posts: 2560
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If a fair die is rolled three times, what is the probability that a 3  [#permalink]

### Show Tags

10
7
zxcvbnmas wrote:
If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?

A) 25/36

B) 125/216

C) 91/216

D) 11/36

E) 36/216

Questions such as these that talk about "at least" or "maximum" or "minimum" in probability questions should make sure realize that probability of any event (N) to occur = 1- P(Not N)

Thus, the probability of at least 1 roll = 1- Probability of NO 3s = 1- (5/6)(5/6)(5/6) = 1-125/216 = 91/216.

5/6 is the probability of NOT getting a 3 in any 1 roll with 5 allowed numbers (=1,2,4,5,6) out of a total of 6 possibilities.

C is thus the correct answer.

Hope this helps.
##### General Discussion
Intern  Joined: 10 Sep 2016
Posts: 15
If a fair die is rolled three times, what is the probability that a 3  [#permalink]

### Show Tags

1
If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?

a 25/36
b 125/216
c 91/216
d 11/36
e 36/216

thanks !!!

Originally posted by geetgmat on 14 Oct 2016, 04:33.
Last edited by abhimahna on 14 Oct 2016, 05:28, edited 1 time in total.
Hided the OE
Intern  Joined: 02 Sep 2016
Posts: 41

### Show Tags

7
1
geetgmat wrote:
If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?

a 25/36
b 125/216
c 91/216
d 11/36
e 36/216

thanks !!!

probability that a 3 occurs on one roll= 1/6
--> probability that a 3 does not occurs on one roll= 1- (1/6) = 5/6

Now, probability that a 3 occurs on at least one roll= 1- (probability that a 3 occurs on none of the 3 rolls)
=1- (5/6 * 5/6 * 5/6) = 1- (125/216) = 91/216

~Consider Kudos if it helped Retired Moderator P
Joined: 19 Mar 2014
Posts: 915
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: If a fair die is rolled three times, what is the probability that a 3  [#permalink]

### Show Tags

2
1
zxcvbnmas wrote:
If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?

A) 25/36

B) 125/216

C) 91/216

D) 11/36

E) 36/216

Probability of 3 occurs $$= \frac{1}{6}$$

Probability of 3 does not occurs $$= \frac{5}{6}$$

Probability of not getting 3 in three dice rolls $$= \frac{5}{6} * \frac{5}{6} * \frac{5}{6}$$

Probability of not getting 3 in three dice rolls $$= \frac{125}{216}$$

Probability of getting 3 in three dice rolls $$= 1 - \frac{125}{216}$$

$$= \frac{(216 - 125)}{216}$$

$$= \frac{91}{216}$$

_________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475
Intern  B
Joined: 12 Jul 2017
Posts: 2
Re: If a fair die is rolled three times, what is the probability that a 3  [#permalink]

### Show Tags

I'm brainfarting right now - how would you go about calculating this the other way, i.e. that the 3 appears at least once?
Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2809
Re: If a fair die is rolled three times, what is the probability that a 3  [#permalink]

### Show Tags

zxcvbnmas wrote:
If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?

A) 25/36

B) 125/216

C) 91/216

D) 11/36

E) 36/216

We can use the following formula:

1 = P(at least one three) + P(no threes)

Let’s determine P(no threes):

5/6 x 5/6 x 5/6 = 125/216

Thus, P(at least one three) is 1 - 125/216 = 91/216.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Current Student B
Joined: 18 May 2016
Posts: 89
Location: India
GMAT 1: 700 Q49 V35 GMAT 2: 700 Q49 V35 WE: Consulting (Non-Profit and Government)
Re: If a fair die is rolled three times, what is the probability that a 3  [#permalink]

### Show Tags

Probability of obtaining 3 = 1/6

Probability of not getting 3 = 1-1/6 = 5/6

Probability of getting 3 at least once = 1- Probability of never getting 3 (Getting 3 once, twice or thrice and Never getting 3 are mutually exclusive events)

Thus, Probability of getting 3 at least once in 3 rolls of die= 1- (Probability of never getting 3 in 3 rolls of die

= 1- (5/)*(5/6)*(5/6)
=1-125/216
=91/216
= Ans
_________________
GMAT chronicles : 670-->660--> 700--> 650--> 680-->660--> 610-->700 (main exam)-->710--740-->700 (main exam again) -->Target 740+

Never never never never NEVER give up!!

I can and I will- watch me.
Senior Manager  G
Joined: 31 May 2017
Posts: 334
Re: If a fair die is rolled three times, what is the probability that a 3  [#permalink]

### Show Tags

Probability of atleast 1 3's = 1 - probability of No 3's
Probability of getting No 3's when rolled out a dice = 5/6

Probability of not getting when dice is rolled 3 times is = 1 - (5/6) (5/6) (5/6) = 91/216

Ans: C
Manager  B
Joined: 02 Jul 2016
Posts: 134
Location: India
GMAT 1: 650 Q49 V28 GPA: 4
Re: If a fair die is rolled three times, what is the probability that a 3  [#permalink]

### Show Tags

3
zxcvbnmas wrote:
If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?

A) 25/36

B) 125/216

C) 91/216

D) 11/36

E) 36/216

Hi
I did it like this:
P(E)=1/6
P(E)'=5/6
So probablity of getting in first roll at any position =1/6*5/6*5/6*3
also this can happen in 2 rolls at any position= 1/6*1/6*5/6*3
and finally at all the 3 positions 1/6*1/6*1/6

So adding these 3 will give us
75/216+15/216+1/216=91/216
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5483
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If a fair die is rolled three times, what is the probability that a 3  [#permalink]

### Show Tags

zxcvbnmas wrote:
If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?

A) 25/36

B) 125/216

C) 91/216

D) 11/36

E) 36/216

P of not getting 3 ; 5/6
so
5/6 *5/6 * 5/6 = 125/216
P of 3
1-125/216
91/216 ; IMO C
Intern  Joined: 21 Sep 2019
Posts: 1
Re: If a fair die is rolled three times, what is the probability that a 3  [#permalink]

### Show Tags

bfistein wrote:
I'm brainfarting right now - how would you go about calculating this the other way, i.e. that the 3 appears at least once?

So to calculate it the other way round,

probability of getting a 3 atleast once - (1/6 * 5/6 * 5/6) * 3 (because it can appear in the 1st 2nd or 3rd roll)
probability of getting two 3s - (1/6 * 1/6 * 5/6) * 3 (can appear in 1st & 2nd, 2nd & 3rd or 1st & 3rd)
probability of getting three 3s - (1/6 * 1/6 * 1/6)

hence ((25*3) + (5*3) + 1)/216 = 91/216 Re: If a fair die is rolled three times, what is the probability that a 3   [#permalink] 27 Sep 2019, 05:10
Display posts from previous: Sort by

# If a fair die is rolled three times, what is the probability that a 3  