A fair six sided die is rolled four times in a row. What is the probability that die will come up six at least once?
Each time we roll a fair six-sided die, there is a 1 in 6 chance that it will come up as a six. We can then use this to figure out what the chance is that a six will be rolled at least once over 4 throws. Because there is often confusion about whether to use addition or multiplication, let's do the math two different ways and see what happens:
The first way is to take each throw and see it as an individual event, each one having a 1 in 6 chance of getting a six, and that there are four of them:
The other way to view it is to say that there are four throws, each with a chance one in six chance of being a six:
How you think about the throws will determine how you do the math.
To get a 6 "at least once", means it can be
There are obviously many combinations in each of these outcomes which will require lengthy calculations!
Note that the only outcome which is NOT included is
There is only ONE combination of this happening.
Not 6 and Not 6 and Not 6 and Not 6
The sum of all the probabilities is always equal to 1.