Originally Posted by

**smoothi963** Three fair six-sided dice are tossed. what is the probability that the sum of the numbers on the two dice equals the number on the third die?

Can someone help me with this please?

Suppose the dice are distingishable and we start by asking what is the

probability that die 1 is equal to the sum on die 2 and die 3.

The table below shows all the ways this can be done.

Code:

Die1 Die2 Die3
2 1 1
3 1 2
3 2 1
4 1 3
4 3 1
4 2 2
5 1 4
5 4 1
5 2 3
5 3 2
6 1 5
6 6 1
6 2 5
6 5 2
6 3 3

There are 15 ways that this can occur. In addition there are 15 ways that

die2 can be equal to the sum of die1 and die3, and 15 ways that die3 can

be the sum of die1 and die2. That's a total of 45 ways out of a total of

6^3 different equaly likley results so the the required probability is:

p = 45/6^3 = 5/24 ~= 0.208

RonL