In a simultaneous throw of a pair of dice, find the probability of getting a total of 9 or more.

When a pair of dice are thrown simultaneously the maximum sum possible is 12.

The possible cases of getting a sum of 9 are:

                    dice 1     dice 2

                    four         five.....................(1)

                    five          four.....................(2)

                     six          three....................(3)

                   three         six.......................(4)  

So a total of 4 cases are possible

The possible cases of getting a sum of 10 are:

                    dice 1     dice 2

                     four        six......................(1)

                      six         four.....................(2)

                     five        five.....................(3)

So a total of 3 cases are possible

The possible cases of getting a sum of 11 are:

                   dice 1       dice 2

                    five           six...................(1)

                     six           five..................(2)

So a total of 2 cases are possible

The possible cases of getting a sum of 12 are:

                  dice 1      dice 2

                   six           six.....................(1)

So a total of 1 case is possible.

Total number ways of getting a sum of 9 or more = 4 + 3 + 2 + 1 = 10 ways

Total outcomes when two dice are rolled simultaneously = 6 * 6 = 36 ways

Probability of getting a sum of 9 or more = Expected number of outcomes/ Total outcomes

= $$\frac{10}{36}$$

= $$\frac{5}{18}$$