Question

You roll two six sided number cubes. What are the possible outcomes? Explain please. Test tommorow

Answer 1

First die: can be any number 1, 2, 3, 4, 5, 6
2nd die: can be any number 1, 2, 3, 4, 5, 6

When you roll both, you must consider that each number of the 1st die can be matched up with any number on the second die. If I write the possible combinations as (1st die, 2nd die), then you can get for example:

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
This is all the combinations resulting when the 1st die is "1" and matching it up to any possible outcome that results from the 2nd die.
You can imagine that you will get 6 more outcomes when the 1st die is a "2" (getting (2, 1), ... (2, 6))

And you continue this way until the 1st die is "6". So, without writing all outcomes explicitely, you would have 36 possible outcomes (i.e \(6 \times 6 = 36\)):

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), ............................, (2, 6)
(3, 1), ......................................, (3, 6)
(4, 1), ......................................, (4, 6)
(5, 1), ......................................, (5, 6)
(6, 1), ......................................, (6, 6)