Question

Two number cubes are rolled --one white and one yellow. How do you find the probability that the white cube shows a 6 and the sum is greater than 9?

Answer 1

`P("white cube" = 6, "sum of both cubes" >9)=3/36=1/12`

Explanation:

I'm going to assume that we're working with fair, standard, 6-sided dice.

Let's look at the possible rolls (I'll highlight the white cube's 6 and sums greater than 9 with `color(blue)"blue"`):

`((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,color(blue)10),(5|,6,7,8,9,10,color(blue)11),(6|,7,8,9,10,11,color(blue)12))`

There are 3 ways we can have the white cube be a 6 and the sum of the two cubes be greater than 9. This is out of 36 possible rolls, and so we can say:

`P("white cube" = 6, "sum of both cubes" >9)=3/36=1/12`