If two fair six-sided dice are thrown, what is the probability that th

Question

If two fair six-sided dice are thrown, what is the probability that the sum of the numbers showing on the dice is a prime number?

(A) 5/11
(B) 5/12
(C) 1/2
(D) 7/12
(E) 7/9

bellcurve · Answer

Prime numbers between 2 to 12 inclusive are 2,3,5,7,11.

One way to get 2 = 1,1
two ways to get 3 = 1,2,&2,1
four ways to get 5 = 2,3&3,2&4,1&1,4
six ways to get 7 = 1,6&6,1&2,5&5,2&3,4&4,3
two ways to get 11 = 5,6&6,5

Total ways to get price = 15

Probability = 15/36 => 5/12

Any short-cut efficient way anybody can think of?

IanStewart · Answer

There really aren't any shortcuts for dice problems, which is why they don't show up on the GMAT. For two dice, the pattern is simple enough to learn, but you won't need to know it on the test. In advanced math, you learn something called 'generating functions' to handle general dice problems, but it wouldn't be at all helpful to know about those for the GMAT.

agdimple333 · Answer

total possibilities = 6 * 6

instances that sum of faces of dice are prime #s -
1, 1
1, 2 and 2,1
1,4 and 4,1
1,6 and 6,1
2,3 and 3,2
2,5 and 5,2
3,4 and 4,3
5,6 and 6,5
total 15 
==> 15/36 = 5/12

dreambeliever · Answer

OA is B.
However, if there are 2 dice and they are thrown together then why do we count (1,2) and (2,1) separately? The question does not specify that the dice look different or that they are thrown one after the other in which case it would have been easier to understand that the order in which numbers appear actually matters. I know this might be very elementaryfor most people as I seem to be only one who had this question but i want to understand it fully.

Thanks!

Posted from my mobile device

satya2029 · Answer

Prime means odd + Special case of 2
(1,3,5) and (2,4,6)
Start from 1 then 3 then 5
(1,2),(1,4),(1,6),(3,2),(3,4),(5,2),(5,6)
7 cases
So total 14 cases as for (2,1) sum is also a prime number
14+special case(1,1)
15 cases
So probability=15/36
5/12
B:)

BrushMyQuant · Answer

Given that two six-sided dice are thrown and we need to find what is the probability that the sum of the numbers showing on the dice is a prime number?

As we are rolling two dice => Number of cases =  6^2  = 36

We know that prime numbers are 2, 3, 5, 7, 11 (between 1+1=2 and 6+6 = 12)

Lets start writing the possible cases where sum of the two rolls = 2, 3, 5, 7 , 11. Following are the possible cases:
(1,1), (1,2), (1,4), (1,6)
(2,1), (2,3), (2,5)
(3,2), (3,4)
(4,1), (4,3)
(5,2), (5,6)
(6,1), (6,5)

=> 15 cases

=> Probability that sum of the numbers showing on the dice is a prime number =  \frac{15}{36}  =  \frac{5}{12}

So,  Answer will be B 
Hope it helps!

Watch the following video to learn How to Solve Dice Rolling Probability Problems

https://www.youtube.com/watch?v=5PVZYQXet18

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