Question 1115482
Roll a pair of fair dice.  Then, find the probability to get a sum on the top surfaces that is less than seven or an odd number.
======================================================

Less than 7:  2,3,4,5,6
Odd numbers:  3,5,7,9,11 <br>

It is the union of these two sets:  S= { 2,3,4,5,6,7,9,11 }  that is of interest. <br>

To find the probability of getting a sum in S, we can look at S', the complement of S:
P(S) = 1-P(S')
S' = { 8, 10, 12 }<br>

There are 36 possible outcomes on the roll of two dice.
There are 5 ways to get an 8:  {6,2}, {5,3}, {4,4}, {3,5}, {2,6}
There are 3 ways to get a 10:  {4,6}, {5,5}, {6,4}
There is one way to get a 12:  {6,6} <br>

In all, S' has 9 ways of occurring, so P(S') = 9/36,  and P(S) = 1-9/36 = 3/4.
—

Ans:   P{sum = 2,3,4,5,6,7,9, or 11} = {{{3/4}}} = 75%.