Question

You roll two number cubes. Find the probability of the sum of the cubes being prime? (Round to 3 decimal places)

Answer 1

`15/36=0.41bar6~=0.417`

Explanation:

The possible rolls are:

`((color(white)(0),ul1,ul2,ul3,ul4,ul5,ul6),(1|,2,3,4,5,6,7),(2|,3,4,5,6,7,8),(3|,4,5,6,7,8,9),(4|,5,6,7,8,9,10),(5|,6,7,8,9,10,11),(6|,7,8,9,10,11,12))`

The sums 2, 3, 5, 7, 11 are prime. There are:

`(("Roll","Ways"),(2, 1),(3,2),(5,4),(7,6),(11,ul2),("Total",15))`

15 ways to achieve a prime sum. The probability therefore of rolling a prime sum is:

`15/36=0.41bar6~=0.417`