Question

A cube is painted red on all six sides, then cut into 125 smaller congruent cubes.

A small cube is selected at random and rolled. What is the probability that it has a red side facing up?

Answer 1

Good problem! I love it.
We have ___ cubes with 3 red sides
We have ___ cubes with 2 red sides
We have ___ cubes with 1 red side
We have ___ cubes with no red sides
How many of each?

Answer 2

Cube has 8 corners, so # w/3 red sides is 8.

Answer 3

# with 2 sides is 36 and # with 1 side is 54 and no sides is 27

Answer 4

I think the # with no red should be 4 x 4 x 4. Do you see why?

Answer 5

No you are right.

Answer 6

So we have them all, I think.

Answer 7

Next step multiply
8/27 x 3/6 etc. and add them up.

Answer 8

Nice job with the calculating, there.

Answer 9

Thanks, so now what do we do.

Answer 10

For each class multiply the P(you choose that class) x P(red given that class) and add them up.

Answer 11

What do you mean (you choose that class)