Question 1194146
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We'll start with P(A).


Let's say we have two dice, one red and the other blue
Each is labeled 1 through 6
The 36 possible dice sums are listed below
<table border=1 cellpadding=10><tr><td>+</td><td><font color=red>1</font></td><td><font color=red>2</font></td><td><font color=red>3</font></td><td><font color=red>4</font></td><td><font color=red>5</font></td><td><font color=red>6</font></td></tr><tr><td><font color=blue>1</font></td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td></tr><tr><td><font color=blue>2</font></td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td></tr><tr><td><font color=blue>3</font></td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td></tr><tr><td><font color=blue>4</font></td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td><td>10</td></tr><tr><td><font color=blue>5</font></td><td>6</td><td>7</td><td>8</td><td>9</td><td>10</td><td>11</td></tr><tr><td><font color=blue>6</font></td><td>7</td><td>8</td><td>9</td><td>10</td><td>11</td><td>12</td></tr></table>Use that table to determine...<ul><li>There are 4 ways to roll a 9</li><li>There are 3 ways to roll a 10</li><li>There are 2 ways to roll an 11</li><li>There is 1 way to roll a 12</li></ul>In all, there are 4+3+2+1 = 10 ways to get a sum that is larger than 8.
This is out of the 36 total outcomes
10/36 = (5*2)/(18*2) = 5/18 = 0.28 is the approximate value of P(A)
Event A happens roughly 28% of the time. 


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Now onto calculating P(B)


Refer to the chart above<ul><li>There is 1 way to roll a 2</li><li>There are 3 ways to roll a 4</li><li>There are 5 ways to roll a 6</li><li>There are 5 ways to roll an 8</li><li>There are 3 ways to roll a 10</li><li>There is 1 way to roll a 12</li></ul>Adding up those frequencies gets us 1+3+5+5+3+1 = 18


Then dividing that over the total 36 outcomes yields 18/36 = 1/2 = 0.50 which is the value of P(B).
This is to be expected since half of the numbers on the die are even, so the sum being even should happen half the time. 


Side notes:
even + even = even
odd + even = odd
odd + odd = even


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Answers:
P(A) = 0.28
P(B) = 0.50
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