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?
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:
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: