**Question:**

When two dice are rolled:

(i) List the outcomes for the event that the total is odd.

(ii) Find probability of getting an odd total.

(iii) List the outcomes for the event that total is less than 5.

(iv) Find the probability of getting a total less than 5?

**Solution:**

Possible outcomes when two dice are rolled :

$\mathrm{S}=\{(1,1),(1,2),(1,3),(1,4), \cdots,(6,5),(6,6)\}$

Therefore, the number of possible outcomes in the sample space is 36 .

(i) The outcomes for the event that the total is odd:

E $=\{(1,2),(1,4),(1,6),(2,1),(2,3),(2,5),(3,2),(3,4),(3,6),(4,1),(4,3),(4,5),(5,2),(5,4),(5,6),(6,1),(6,3),(6,5)\}$

(ii) The number of favourable outcomes is 18 .

$\therefore \mathrm{P}(\mathrm{E})=\frac{18}{36}=\frac{1}{2}$

(iii) The outcomes for the event that total is less than 5 :

$\mathrm{B}=\{(1,1),(1,2),(1,3),(2,1),(2,2),(3,1)\}$

(iv) The number of favourable outcomes is 6 .

$\therefore P(B)=\frac{6}{36}=\frac{1}{6}$