Thread: 5 dice probability

I need to know the fomula to find what the probability of rolling 5 dice one time each and getting a 5 of a kind, 4 of a kind, 3 of a kind, pair, and a straight. I believe the forumula for 5 of a kind is 6*(1/6*1/6*1/6*1/6*1/6) equalling a 6/7776 chance of 5 of a kind. What is the formula to get the other answers?

Originally Posted by Susan0814

I need to know the fomula to find what the probability of rolling 5 dice one time each and getting a 5 of a kind, 4 of a kind, 3 of a kind, pair, and a straight. I believe the forumula for 5 of a kind is 6*(1/6*1/6*1/6*1/6*1/6) equalling a 6/7776 chance of 5 of a kind. What is the formula to get the other answers?

5 of a kind

First Roll) Anything thus 1/1

Second Roll) Must match #1 thus 1/6

Third, Fourth, Fifth Roll) Must math #1 thus 1/6

Hence (1)(1/6)(1/6)(1/6)(1/6) = 1/1296

I have the possibility of rolling a 5 of a kind. What is the formula needed to get the probability of 4 out of 5, 3 out of 5, a pair and a straight. Do I need to adjust the one I used to get the 5 of a kind and how do I do that?

I am rolling 5 dice one time and trying to find the odds of rolling a 4 of a kind then rolling all 5 dice again for the 3 of a kind, etc.

4 of a Kind
There are 6 possibilities: 4 1's, 4 2's , ... 4 6's.
Let us do the specific case 4 1's and then multiply by 6 after we find that specific probability.

The probability of getting 4 1's (exactly not 5) is one of the following:
1111X
111X1
11X11
1X111
X1111

Let us find the probability just for the first specific case:
1111x which is (1/6)(1/6)(1/6)(1/6)(5/6) = 5/1296

Multiply by 5 again (for all cases)

25/1296 is probability to get 4 ones exactly.

Now multiply by 6 to get the probabilities of the other cases which can happen:

25/216