Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss! Oct 26 07:00 AM PDT  09:00 AM PDT Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to prethink assumptions and solve the most challenging questions in less than 2 minutes.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 08 Sep 2010
Posts: 150
Location: India
WE 1: 6 Year, Telecom(GSM)

If four dice are thrown together , then the probability that the sum
[#permalink]
Show Tags
28 Oct 2010, 02:53
Question Stats:
29% (01:08) correct 71% (02:13) wrong based on 19 sessions
HideShow timer Statistics
If four dice are thrown together , then the probability that the sum on them together is either 19 or 23 1. 4/108 2. 12/108 3. 9/108 4. 5/108 5. 6/108
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Consider KUDOS if You find it good



Intern
Joined: 26 Mar 2010
Posts: 26

Re: If four dice are thrown together , then the probability that the sum
[#permalink]
Show Tags
28 Oct 2010, 07:29
Is the answer 5/108? Just want to make sure so that I don't explain a wrong answer and confuse people...



Intern
Joined: 30 Sep 2010
Posts: 47

Re: If four dice are thrown together , then the probability that the sum
[#permalink]
Show Tags
28 Oct 2010, 07:41
no of ways to get 19 = no of ways to get 9 = C(8,5) = 56 no of ways to get 23 = no of ways to get 5 = C(4,1) = 4
So total ways = 60 probability = 60/1296 = 5/108 (I need kudos)
Find the simpler way
Dice problem
A nice way to find the sum:
e.g 4 dices are thrown
then the outcome of the sums can be:
4,5,6,………………14……………..,22,23,24
Mid point is 14. The left side of the mid point is mirror image of the right part.
So lets say the probability of getting a 20 is same as the probability of getting a 8
In this case the number of ways to get the sums are:
4: C(3,0) = 1 (start 1 before the # of throws) 5: C(4,1) = 4 6: C(5,2) = 10 7: C(6,3) = 20 8: C(7,4) = 35
So probability of getting a 20 = probability of getting a 8 = 35/6^4 = 35/1296 Similarly for rolloing of 3 dices:
then the outcome of the sums can be: Mid point is 10.5. The left side of the mid point is mirror image of the right part.
3,4,5,6,………………10.5……………..,15.16.17.18
In this case the number of ways to get the sums are:
3: C(2,0) = 1 (start 1 before the # of throws) 4: C(3,1) = 3 5: C(4,2) = 6 6: C(5,3) = 10 7: C(6,4) = 15 8: C(7,5) = 21



Manager
Joined: 27 Mar 2010
Posts: 77

Re: If four dice are thrown together , then the probability that the sum
[#permalink]
Show Tags
28 Oct 2010, 20:25
krushna wrote: no of ways to get 19 = no of ways to get 9 = C(8,5) = 56 no of ways to get 23 = no of ways to get 5 = C(4,1) = 4
So total ways = 60 probability = 60/1296 = 5/108 (I need kudos)
Find the simpler way
Dice problem
A nice way to find the sum:
e.g 4 dices are thrown
then the outcome of the sums can be:
4,5,6,………………14……………..,22,23,24
Mid point is 14. The left side of the mid point is mirror image of the right part.
So lets say the probability of getting a 20 is same as the probability of getting a 8
In this case the number of ways to get the sums are:
4: C(3,0) = 1 (start 1 before the # of throws) 5: C(4,1) = 4 6: C(5,2) = 10 7: C(6,3) = 20 8: C(7,4) = 35
So probability of getting a 20 = probability of getting a 8 = 35/6^4 = 35/1296 Similarly for rolloing of 3 dices:
then the outcome of the sums can be: Mid point is 10.5. The left side of the mid point is mirror image of the right part.
3,4,5,6,………………10.5……………..,15.16.17.18
In this case the number of ways to get the sums are:
3: C(2,0) = 1 (start 1 before the # of throws) 4: C(3,1) = 3 5: C(4,2) = 6 6: C(5,3) = 10 7: C(6,4) = 15 8: C(7,5) = 21 Hi, thanks for the solution But how u got no of ways to get 9 = C(8,5), what i don't understand is how to think about c(8,5) quickly??? for sum of 4(in case of 4 dices) i can understand that no of ways=1 because each dice=1 then sum=4. but didn't understand why have to written it as c(3,0)???



Intern
Joined: 30 Sep 2010
Posts: 47

Re: If four dice are thrown together , then the probability that the sum
[#permalink]
Show Tags
28 Oct 2010, 21:06
the formula I came up with is based on the pattern of the number of ways. I mean I first got the answers in the normal way(by calculating all the possibilities) and then I noticed a certain pattern and finally devised this formula. You can think, its my PATENT but I am sure this works for everything. I explained in my example about the pattern. This will help you to get the answer to any SUM problem in 1 minute. GMAT is all about saving time. If you have problem in understanding the pattern, shoot another question and I will answer it with the formula



Manager
Joined: 27 Mar 2010
Posts: 77

Re: If four dice are thrown together , then the probability that the sum
[#permalink]
Show Tags
28 Oct 2010, 21:28
krushna wrote: the formula I came up with is based on the pattern of the number of ways. I mean I first got the answers in the normal way(by calculating all the possibilities) and then I noticed a certain pattern and finally devised this formula. You can think, its my PATENT but I am sure this works for everything. I explained in my example about the pattern. This will help you to get the answer to any SUM problem in 1 minute. GMAT is all about saving time. If you have problem in understanding the pattern, shoot another question and I will answer it with the formula Thanks a lot, I got it... +1 to you



Retired Moderator
Joined: 02 Sep 2010
Posts: 726
Location: London

Re: If four dice are thrown together , then the probability that the sum
[#permalink]
Show Tags
28 Oct 2010, 22:34
If you are curious where these results come from, read : http://mathworld.wolfram.com/Dice.html This is well beyond the scope of the exam though. And personally I am not a proponent of remembering too many formulae. Posted from my mobile device
_________________



Intern
Joined: 08 May 2010
Posts: 10

Re: If four dice are thrown together , then the probability that the sum
[#permalink]
Show Tags
29 Oct 2010, 08:37
What is the source of this question?
Could this really be a GMAT question?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India

Re: If four dice are thrown together , then the probability that the sum
[#permalink]
Show Tags
29 Oct 2010, 11:28
sjgudapa wrote: What is the source of this question?
Could this really be a GMAT question? You could get a question such as 'If four dice are thrown together , then the probability that the sum on them is 23 is .....' This is a simple question where you do not need to do laborious calculations. You just need to use logic. The chances of the original question featuring in GMAT are pretty slim. Remember, you need to solve a question in under two minutes on average. And they definitely do not expect you to remember formulas other than the standard ones such as area of circle etc.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1806

Re: If four dice are thrown together , then the probability that the sum
[#permalink]
Show Tags
29 Oct 2010, 15:49
krushna wrote: You can think, its my PATENT You can't patent something that de Moivre came up with 270 years ago To solve general 'dice sum' problems, mathematicians use what are known as 'generating functions'. Those are miles and miles beyond the scope of the GMAT. Dice sums are generally very awkward to work out except in special cases. As Karishma pointed out, it's not hard to count the number of ways to get a sum of 23, because that's an extreme case  you must get three 6's and a 5. To count the number of ways to get a 19 is much more timeconsuming, however, and is definitely not the type of thing you'll ever need to do on the GMAT. It's very unlikely you'd even be asked the probability of getting a sum of 23 on the GMAT, not because the question is too difficult, but rather because the question is too 'boring'; you can only do it by 'brute force' enumeration. Most GMAT counting/probability questions contain some kind of twist, trick or shortcut that makes them more 'interesting' than your standard 'plug numbers into a formula' question that any spreadsheet could solve. That's one of the reasons I completely agree with shrouded's caution above about memorizing formulas  the GMAT is simply not a test of how many formulas you can remember.
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2815

Re: If four dice are thrown together , then the probability that the sum
[#permalink]
Show Tags
22 Feb 2018, 17:45
ankitranjan wrote: If four dice are thrown together , then the probability that the sum on them together is either 19 or 23
1. 4/108 2. 12/108 3. 9/108 4. 5/108 5. 6/108 Notice that the probability of getting a sequence of 4 numbers in a specific order, e.g., 1234, is 1/6 x 1/6 x 1/6 x 1/6 = 1/6^4. Now let’s list all the groups of 4 numbers that add up to 19 with the number of ways the numbers within a group can be arranged in parenthesis: 6661 (4!/3! = 4) 6652 (4!/2! = 12) 6643 (4!/2! = 12) 6553 (4!/2! = 12) 6544 (4!/2! = 12) 5554 (4!/3! = 4) Thus the probability of getting a sum of 19 is (4 x 2 + 12 x 4) x 1/6^4 = 56/6^4. Similarly, let’s list all the groups of 4 numbers that add up to 23 with the number of ways the numbers within a group can be arranged in parenthesis: 6665 (4!/3! = 4) We see that there is only one group of 4 numbers that add up to 23 and within this group, there are 4 ways to arrange them. Thus the probability of getting a sum of 23 is 4 x 1/6^4 = 4/6^4. Thus the probability of getting a sum of 19 or 23 is 56/6^4 + 4/6^4 = 60/6^4 = (6 x 10)/6^4 = 10/6^3 = 10/216 = 5/108. Answer: D
_________________
5star rated online GMAT quant self study course 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.




Re: If four dice are thrown together , then the probability that the sum
[#permalink]
22 Feb 2018, 17:45






