Here's something from a manhattan study guide... What is the

Question

Here's something from a manhattan study guide...

What is the probability that the sum of two dice will yield a 4 or 6?

asdert · Answer

(Chances of getting a 4 + Chances of getting a 6) / Total number of possibilities ===>

3+5/36 = 8/36 = 2/9, because:

Chances of getting a 4: 3+1, 2+2, 1+3
Chances of getting a 6: 5+1, 4+2, 3+3, 2+4, 1+5
Number of possibilities: 6 x 6

giantSwan · Answer

your correct. what am I doing wrong...by the same logic I employed

Chances of getting a 4: 3+1, 2+2, 2+2, 1+3
Chances of getting a 6: 5+1, 4+2, 3+3, 3+3, 2+4, 1+5
Number of possibilities: 6 x 6

shouldn't the 2+2 and 3+3 repeat for each die since they are unique?

walker · Answer

Yes, 2+2 does not differ form 3+1 (if we consider 3+1 and 1+3 as different options)

asdert · Answer

There's only one 2 in each die, therefore only only possibility for 2+2. What 
you are doing is the same thing as counting twice 3+1, 3+1.

Does it help to think of it in this way?
What are the chances of getting 2 twice in a row:
(1/6)(1/6)=2/36

Oski · Answer

Nope, I think that they actually differ. 2+2 is ONE of the 36 possibilities. 1+3 and 3+1 are TWO of them

You can write down the 36 possibilities if you want to be sure of that :

{1,1} {2,1}  {3,1}  {4,1}  {5,1}  {6,1} 
{1,2}  {2,2}  {3,2}  {4,2}  {5,2} {6,2} 
 {1,3}  {2,3}  {3,3}  {4,3} {5,3} {6,3} 
{1,4}  {2,4}  {3,4} {4,4} {5,4} {6,4} 
 {1,5}  {2,5} {3,5} {4,5} {5,5} {6,5} 
{1,6} {2,6} {3,6} {4,6} {5,6} {6,6}

(bolded are the possibilities that lead to a sum of 4 or 6, you can verify there are 8 of them)

As said above, answer is 8/36 = 2/9

walker · Answer

They differ if only you consider 2,2 and 1,3 without order, otherwise, 2+2 does not differ form 1+3, because probability for both options is 1/36

Oski · Answer

It differs because counting 1+3 and its reverse is not double counting, whereas counting 2+2 and its reverse is.

If you try to count "without order", the events are not equiprobable any more and you cannot apply the formula "number of occurrences of the event / number of total possibilities"

pavitravenkitesh · Answer

i got the answer 8/36 .. is that right???

walker · Answer

we are talking about the same thing but in other words

Oski · Answer

Yes, I just realized it

But not giantSwam

giantSwan · Answer

Thanks, this discussion was very helpful. I understand now.

iamcartic · Answer

2/9

4 : 1+3, 2+2, 3+1 = 3/6x6

6: 1+5, 2+4, 3+3, 4+2, 5+1 = 5/6x6

P of a or b = Pa + Pb = 2/9

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