Question

Lenny rolls two number cubes. What is the probability that the sum of the the numbers Lenny rolls is either 4 or 7?

Answer 1

Prob(`4 or 7`)=1/4=25%#

Explanation:

We can assume without loss of generality that one die is `color(red)("red")` and the other die is `color(blue)("blue")`

There are `color(green)(36)` possible outcomes (since for each of the `color(red)(6)` possible `color(red)("red")` outcomes there are `color(blue)(6" blue")` outcomes.

The outcomes that result in a total of `4` or `7`

#{: (color(red)("red"),color(blue)("blue")), (color(red)(1),color(blue)(3)), (color(red)(2),color(blue)(2)), (color(red)(3),color(blue)(1)), (color(red)(1),color(blue)(6)), (color(red)(2),color(blue)(5)), (color(red)(3),color(blue)(4)), (color(red)(4),color(blue)(3)), (color(red)(5),color(blue)(2)), (color(red)(6),color(blue)(1)) :}#

for a total of `color(brown)(9)` outcomes that result in `4` or `7`

`"Prob"(4 or 7) = color(brown)(9)/color(green)(36) = 1/4`