Question

A red number cube and a blue number cube are rolled. If all numbers are equally likely, what is the probability that the number on the red cube is greater?

Answer 1

`P(R>B) = 15/36 = 5/12`

Explanation:

The clearest way to work this out is with a possibility space.

"Y" indicates that the value on the red is greater than on the blue.

`color(red)(6)" " Y" "Y" "Y" "Y" "Y`
`color(red)(5)" " Y" "Y" "Y" "Y`
`color(red)(4)" " Y" "Y" "Y`
`color(red)(3)" " Y" "Y`
`color(red)(2)" " Y`
`color(red)(1)`
`color(blue)( " " 1" "2" "3" "4" "5" "6")`

There are `6xx6 = 36` possible outcomes when throwing 2 dice.

For 6 of these, the values are the same, when a 'double' is thrown.

For the 30 outcomes that are left, in half of them, the red value is more, and in half of them the blue value is more.

`30/2 = 15`

The 15 outcomes where red > blue are shown above.

`P(R>B) = 15/36 = 5/12`