Two standard dice are rolled. Whats the probability the difference between the two numbers on the dice is 2?

Answer 1

I assume you subtract the smaller die from the larger in all cases:

Enumerate the possible rolls:
There are 36 possible rolls. And the only way to get a difference of 2 is:
1 3
2 4
3 1
3 5
4 2
4 6
5 3
6 4

That's 8 possible ways out of 36:

8/36 = 2/9

Another way to look at is, you have 4 possible choices for the smaller die (1, 2, 3, 4) which means the larger die will have to be (3, 4, 5, 6). But because the smaller die could be the first or the second, you need to multiply these 4 ways by 2.

8 ways / 36 possible outcomes = 2/9

P.S. Here's the full list of outcomes:
1,1 = 0
1,2 = 1
1,3 = 2 *
1,4 = 3
1,5 = 4
1,6 = 5
2,1 = 1
2,2 = 0
2,3 = 1
2,4 = 2 *
2,5 = 3
2,6 = 4
3,1 = 2 *
3,2 = 1
3,3 = 0
3,4 = 1
3,5 = 2 *
3,6 = 3
4,1 = 3
4,2 = 2 *
4,3 = 1
4,4 = 0
4,5 = 1
4,6 = 2 *
5,1 = 4
5,2 = 3
5,3 = 2 *
5,4 = 1
5,5 = 0
5,6 = 1
6,1 = 5
6,2 = 4
6,3 = 3
6,4 = 2 *
6,5 = 1
6,6 = 0

Answer 2

I'm only going to do the first two problems since it seems like you want us to do your entire homework. 1) Since you can choose a combination of skis, bindings, and boots, you have 8 * 6 * 7 options, or 336 total options. 2) You can get a 5 from the following combinations: 2 + 3 4 + 1 1 + 4 3 + 2 Since you can roll a total of 36 combinations with two dice, and since you have four combinations above, that means that you have a 4/36 chance, or 1/9 chance of rolling a sum of 5.

Answer 3

Well, probability is simply the number of occurences of an certain type of event divided by the total number of possible outcomes for all events.

Since there are 6 possible out comes for each die and the result of each die is presumed to be independent of the other (if it isn't, you'd better have some explaining to do), there are 6x6 or 36 possible outcomes.

Count up the number of possible outcomes that have a difference of two between the two dice, and divide that number of occurrences by 36. Btw, an occurrence of 1 on the first die and 3 on the second die is a DIFFERENT occurrence than 3 on the first die and one on the second die.

Answer 4

the probability of rolling any number on 1 die is 1 in 6

the probability of rolling any particular pair is 1 in 6 times by 1 in 6 so 1 in 36 - 1/36 is a probability of 0.0277777777

count the possible incidences of 2 difference
1-3 2-4 3-5 4-6 3-1 4-2 5-3 6-4 which is 8

8x 0.0277777777 = 0.222222222

Answer 5

whats different between 2 numbers 1 and 4

Answer 6

Possible combinations of difference 2:
1,3
3,1
2,4
4,2
3,5
5,3
4,6
6,4

8 combinations out of a possible 36 (6*6)
= 8/36 or 2/9.

Hope this is right!

Answer 7

2 in 9, or 22.222222%
(see someone did it the long way round)

Answer 8

13
24
31
35
42
46
53
64
so there are eight ways it can happen (out of 36). so it is 22.2 recurring %