There are 3 6-sided dice; 2 red and 1 purple. All three dice are rolled...

[sojeee]

There are 3 dice. (6 sided)
There are 2 red dice and 1 purple die.
All three dice are rolled.
What is the probability that the sum of the number on the 2 red dice makes the number on the purple dice?


P.S- the answer is 5/72 but I don’t know how to work to there

 

[tkhunny]

\(\displaystyle \sum x\cdot p(x)\) -- Why is anything but the most fundamental principal needed?

x = 1 on Purple, (1 on two red) = 0
x = 2 on Purple, ...

Continue in this way...

 

[Guy_that_Minors_in_Maths]

Every die has 1/6 chance of coming up any number from 1 to 6. Since you have 3 of them, you have 6x6x6=216 possibilities, and 1/216 chance for any spesific sequence, for instance (1,1,1).

What you need is two numbers equaling the third one, so that means choose 2 numbers that will equal to 6 at most. There are 15 ways to do it:
(1,1,2) (1,2,3) (1,3,4) (1,4,5) (1,5,6) (2,1,3) (2,2,4) (2,3,5) (2,4,6) (3,1,4) (3,2,5) (3,3,6) (4,1,5) (4,2,6) (5,1,6)

As you can see, all we did is, we started from 1&1 and kept adding 1 to the second die until the sum reached 6. Then we started from 2&1 and so on.
15/216 when simplified by 3 equals 5/72.