Thread: Six-Sided Dice Probability - Getting a 5 or 6

What are the chances of four of X (variable) rolled six-sided dice producing a result of “5” or “6” in one roll?
4 dice = 1.2%
5 dice = ???
6 dice = ???
etc.

I know that each die has a 1 out of 3 (or 1/3, or 33.4%) chance of producing the desired result of 5 or 6 (also called a "hit"). I know that the chances of all four dice of a four-die roll "hitting" is equal to the chance of one of them hitting times the chance of each other one hitting, i.e.
(1/3)*(1/3)*(1/3)*(1/3)

Thank you for your time and your help!

Originally Posted by jpmadigan1

What are the chances of four of X (variable) rolled six-sided dice producing a result of “5” or “6” in one roll?
4 dice = 1.2%
5 dice = ???
6 dice = ???
etc.!

I simply do not understand.

Are you asking: If we roll seven dice, what is the probably getting at least one 5 or 6?

OR, Are you asking: If we roll seven dice, what is the probably getting at exactly four 5's or 6's?

Or is it some else all together?

If we roll seven dice, what is the probability of getting exactly four 5's or 6's.

Sorry for the ambiguity.

Originally Posted by jpmadigan1

If we roll seven dice, what is the probability of getting exactly four 5's or 6's.
Sorry for the ambiguity.

If is the number are dice rolled the probability of getting exactly four 5's or 6's is:


where