Question

Suppose that four 9-sided dice are tossed. What is the probability that the sum on the four dice is greater than or equal to 6?

Answer 1

`P("sum" >=6)=1-5/6561=6556/6561~=99.92%`

Explanation:

The probability can be expressed this way:

`P("sum" >=6)=1-"number of ways to get 5 and less"/"number of ways we can roll 4 9-sided dice"`

How many different ways can we get 5 or less?

We can get the following arrangements and achieve 5 or less:

`1,1,1,1=> 1 " way to achieve"`
`2,1,1,1=> 4 " ways to achieve"`

So there are a total of 5 ways to get a 5 or less.

How many different results can we get rolling the 4 9-sided dice? Each die has 9 possibilities, so we have `9xx9xx9xx9=9^4=6561`

And so we get:

`P("sum" >=6)=1-5/6561=6556/6561~=99.92%`