probability

[danabr07]

this doesn't make sense to me. If 2 number cubes are thrown, find the probability that the sum of the numbers that result is 5 or an even number. my teacher says the answer should be 11/18, but I can't get it to work.

 

[pka]

What are "number cubes"?
Are the just dice?

 

[soroban]

Hello, danabr07!

If 2 number cubes are thrown, find the probability that the sum of the numbers that result is 5 or an even number.
My teacher says the answer should be 11/18, but I can't get it to work.

Have you ever worked with a pair of dice before?

Each die can turn up any of six numbers: {1,2,3,4,5,6}.
. . There are \(\displaystyle 6\,\times6\,=\,36\) possible outcomes.
Usually, there is no formula for working out dice probabiltiies; we must make a list.

Here are the 36 outcomes:
. . \(\displaystyle (1,1)\;\;(1,2)\;\;(1,3)\;\;(1,4)\;\;(1,5)\;\;(1,6)\)
. . \(\displaystyle (2,1)\;\;(2,2)\;\;(2,3)\;\;(2,4)\;\;(2,5)\;\;(2,6)\)
. . \(\displaystyle (3,1)\;\;(3,2)\;\;(3,3)\;\;(3,4)\;\;(3,5)\;\;(3,6)\)
. . \(\displaystyle (4,1)\;\4,2)\;\4,3)\;\4,4)\;\4,5)\;\4,6)\)
. . \(\displaystyle (5,1)\;\;(5,2)\;\;(5,3)\;\;(5,4)\;\;(5,5)\;\;(5,6)\)
. . \(\displaystyle (6,1)\;\;(6,2)\;\;(6,3)\;\;(6,4)\;\;(6,5)\;\;(6,6)\)

Now just count up the ones you want . . .