What is the probability of rolling 2 dice, and getting a total of 7 both times, on two consecutive rolls?

Question

"What is the probability of rolling 2 dice, and getting a total of 7 both times, on two consecutive rolls?"

Ok, I know you gotta make a quick diagram sorta thing (I don't know any other way to calculate the possible outcomes of a two-die roll, so I guess it will work alright...)
Then basically put X's where the totals equal 7, sorta like this...


1 2 3 4 5 6
1 X
2 X
3 X
4 X
5 X
6 X

So out of 36 outcomes, 6 appear to be desired (equal to 7).
So 1/6 equals the probability for 1 two-dice roll equalling 7.

So then just multiply it by itself for the probability for 2 two-dice roll equalling 7?

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Please verify this and also please answer if there is a more efficient way to determine how many desired outcomes there are, rather than graphing it out...

Ah, crud... the format was auto-edited to delete the spaces in my graph. oh well, I think you know where they go.

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And hey...maybe I'm wrong...because the graph doesn't account for a 1 showing up on both dice as two seperate possible outcomes (1,1 or 1,1 / 2,2 or 2,2...etc......looks the same, but technically, wouldn't they be different possible outcomes, thus effecting probability? just as much as 2,3 and 3,2 are two seperate probabilities?)
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Answer 1

I think it's 1/12 because the maximum total you can roll is 12

Answer 2

You're correct. The two rolls of the dice are independent. So, the probability of both events occuring is the product of each event occurring separately.

On each roll, there is a 1 out of 6 chance of getting a seven. The probability of getting 7 on two consecutive rolls is 1/6 x 1/6, or 1 out of 36.

There's really not an easier way to determine the possible outcomes, especially with a pair of dice. You just have to list them all and count them up.

Answer 3

The chances of getting 7 are 1 in 6, so the chances of getting it twice are 1 in 36.

Answer 4

because the two rolls are independent you are correct in that you only need to multiply the two probabilities together to get the solution. the probability of roll two fair die to get a sum of 7 on two consecutive rolls is 1/36

Answer 5

I'm not to good at math so this is what i'll do:

I have two dice right now.....I'll keep rolling them until this happens and then i'll get back to you!! :-)