GMATPrep Probability

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voodoo_child: Master | Next Rank: 500 Posts; Posts: 405; Joined: Thu Feb 10, 2011 1:44 amFollowed by: 1 member; Thanked: 3 times

by voodoo_child » Wed Jun 13, 2012 4:23 am

A pair of standard 6-sided dice is rolled. What is the probability that the sum of
the two dice is equal to 8?
A) 1/9
B) 1/8
C) 5/36
D) 1/6
E) 7/36

OA - C). Why is it not D?

Essentially, the number of ways one can get '8' = (2,6); (3,5) ;(4,4) ; (4,4); (5,3) and (6,2)

Why did I chose (4,4) two times? In the denominator, we have accounted for (4,4) two times because of fundamental principle of counting.

Please help .....

Thanks

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Source: Beat The GMAT — Problem Solving | Wed Jun 13, 2012 4:23 am

coolhabhi: Master | Next Rank: 500 Posts; Posts: 141; Joined: Tue Oct 04, 2011 5:17 am; Thanked: 25 times

by coolhabhi » Wed Jun 13, 2012 5:01 am

No. In the denominator you have not counted (4,4) two times.

Have a look at this.

if the first dice is 1 then the second dice can be any of {1,2,3,4,5,6}.
so your pairs will be (1,1)(1,2)(1,3)(1,4)(1,5)(1,6)

Now similarly if the first dice shows up 2 then the second dice can show up any of {1,2,3,4,5,6}.
so your pairs will be (2,1)(2,2)(2,3)(2,4)(2,5)(2,6)

Similarly write down all the possibilites and you wont get (4,4) counted twice.

Does this explain your question?

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Jun 13, 2012 6:43 am

Another way to think of it is to make the 2 dice different colors: red and blue

So, the outcome red die = 2 and blue die = 6 is different from the outcome red die = 6 and blue die = 2.
However, the outcome red die = 4 and blue die = 4 is the same as the outcome red die = 4 and blue die = 4.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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pavangmat: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Sat Jun 02, 2012 1:58 pm

by pavangmat » Wed Jun 13, 2012 10:23 am

Can anyone explain little more detail of the above problem since I am stuck with this Quant question?

Thanks,
Pavan

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1947: Master | Next Rank: 500 Posts; Posts: 215; Joined: Sat Jun 14, 2008 4:24 pmFollowed by: 1 member; Thanked: 13 times

by 1947 » Wed Jun 13, 2012 10:40 am

possible options that will sum up to 8 are:
2,6 prob of 2 is 1/6 same for 6 so there joint probability is 1/6*1/6=1/36
3,5 1/36 for reason mentioned above
4,4 1/36 for reason mentioned above
5,3 1/36 for reason mentioned above
6,6 1/36 for reason mentioned above

so the sum is 5/36

If my post helped you- let me know by pushing the thanks button. Thanks

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