What is the probability that when we roll four fair 6-sided dice, they won't all show the same number?
Ah...I see the flaw in my reasoning......try this.....
The probability that they don't all show the same number is 1 minus the probability that they DO all show the same number.
But there are only 6 ways that they all show the same number.
So
1 - 6/1296 = 1290 / 1296 = 25/26 = about 99.5%
There are six things possible for the first die, five for the second, four for the third and three for the fourth.
And there are 6^4 = 1296 total possible outcomes for rolling four dice.
So
[6 x 5 x 4 x 3 ] / 1296 = 360 / 1296 = 5/18 = about 28%
Ah...I see the flaw in my reasoning......try this.....
The probability that they don't all show the same number is 1 minus the probability that they DO all show the same number.
But there are only 6 ways that they all show the same number.
So
1 - 6/1296 = 1290 / 1296 = 25/26 = about 99.5%