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?

1 Answer
Sep 2, 2016

#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#