Question

Find the probability that the sum is as stated when a pair of dice is rolled.odd and less than 5

Answer 1

Each die has six possible equiprobable states $x= 1,2,3\dots 6$ and $y = 1,2,3\dots 6$. 

Since the dies are independent, $6*6 = 36$ , unique states $(x,y)$ are possible.

The possible states when the sum is odd and less than 5 are:

$(x,y) = \{(1,2),(2,1)\}$ .

Only 2 states are possible.

Thus, the probability that the sum is odd and less than 5 is:

$\frac{\textrm{number of states when the sum is odd and less than 5} }{\textrm{number of all possible states}} = \frac{2}{36} = \frac{1}{18}$ .