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.
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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 3 ways to get an 8:  {5,3},{3,5}, {4,4}
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 7 ways of occurring, so P(S') = 7/36,  and P(S) = 1-7/36 = 29/36.
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Ans:   P{sum = 2,3,4,5,6,7,9, or 11} = {{{ highlight(29/36) }}} (approx. 0.806).

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EDIT:  Oh thanks tutor ikleyn, I missed 8 = 6+2 = 2+6, so that adds two to S' making P(S')= 9/36 and P(S)=27/36=3/4.