Question

Suppose that a red die and a green die are tossed and the numbers on the sides that face upward are observed. ​(a) what is the probability that the sum of the numbers is less than 4

Answer 1

First of all, let's count how many events compose our sample space: since we are rolling two dice, and each of them has six sides, the sample space has 36 possible events, given by all couples $(x,y)$, with $x,y \in \{1,2,3,4,5,6\}$

Then, we observe that none of the die can give 4 or more, otherwise the sum of the two dice would be at least 5.

So, we have the following possible outcomes:

Red die gives 1, green die gives 3

Both dice give 2

Red die gives 3, green die gives 1.

These are three events out of the 36 possible events, so their probability is

$\cfrac{3}{36} = \cfrac{1}{12}$