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

 It is currently 24 May 2019, 14:49

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

Three six faces fair die are thrown together.What is the probability

Author Message
Intern
Joined: 01 Jan 2016
Posts: 28
Three six faces fair die are thrown together.What is the probability  [#permalink]

Show Tags

24 Jul 2017, 11:25
00:00

Difficulty:

(N/A)

Question Stats:

33% (02:41) correct 67% (06:05) wrong based on 3 sessions

HideShow timer Statistics

Three six faces fair die are thrown together.What is the probability that the sum of the numbers appearing on the die is 12?
(a) 27/216
(b) 25/216
(c) 23/216
(d) 17/216
(c) 24/216

A pretty easy problem, if one can find out the sum of numbers adding to 12 without listing. Any suggestions?

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Director
Joined: 13 Mar 2017
Posts: 724
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: Three six faces fair die are thrown together.What is the probability  [#permalink]

Show Tags

24 Jul 2017, 11:35
theperfectgentleman wrote:
Three six faces fair die are thrown together.What is the probability that the sum of the numbers appearing on the die is 12?
(a) 27/216
(b) 25/216
(c) 23/216
(d) 17/216
(c) 24/216

A pretty easy problem, if one can find out the sum of numbers adding to 12 without listing. Any suggestions?

Total number of events = 6*6*6 = 216
To get the number 12 we will have to pair up the numbers on the die
Number = 1 on 1st die {156,165} Total 2
Number =2 on 1st die {246 , 264, 255} Total 3
Number = 3 on 1st die {363, 336, 354, 345} Total 4
Number = 4 on 1st die {462, 426, 453, 435, 444} Total 5
Number = 5 on 1st die {561, 516, 552, 525, 543, 534} Total 6
Number = 6 on 1st die {651, 615, 642, 624, 633} Total 5

So Number of events of getting 12 = 25

Probability = 25/216

_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3386
Location: India
GPA: 3.12
Three six faces fair die are thrown together.What is the probability  [#permalink]

Show Tags

24 Jul 2017, 11:45
theperfectgentleman wrote:
Three six faces fair die are thrown together.What is the probability that the sum of the numbers appearing on the die is 12?
(a) 27/216
(b) 25/216
(c) 23/216
(d) 17/216
(c) 24/216

A pretty easy problem, if one can find out the sum of numbers adding to 12 without listing. Any suggestions?

With listing, possibly the easiest method.
For sum to be 12 with three dice, we could have a {(1,5,6),(2,4,6),(2,5,5),(3,3,6),(3,4,5),(4,4,4)}

For the combinations (1,5,6),(2,4,6) and (3,4,5) : There are 3! ways of arranging these numbers, $$3*3! = 18$$

For combinations (2,5,5),(3,3,6) : There are $$\frac{3!}{2!}$$ ways of arranging these numbers, $$2*\frac{3!}{2!} = 6$$

There is only one way of arranging the (4,4,4) combination
There are a total of 25 favourable combinations.

The denominator for the probability is 6*6*6 = 216

Probability(sum appearing on three die is 12) : $$\frac{18+6+1}{216} = \frac{25}{216}$$(Option B)

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________
You've got what it takes, but it will take everything you've got
Three six faces fair die are thrown together.What is the probability   [#permalink] 24 Jul 2017, 11:45
Display posts from previous: Sort by