<PRE><B>Question 1193150</B>
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Suppose you roll a pair of six-sided dice and add their totals.
1. What is the probability that the sum of the numbers on your dice is an even number or a number less than 6?
2. What is the probability that the sum of the numbers on your dice is a prime number or a number greater than 5?
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&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;Solution to part &amp;nbsp;(1)



&lt;pre&gt;
When rolling a pair of dice, there are 36 possible outcomes, in all, each with probability of  {{{1/36}}}.


Of them, favorable are those pairs where the sum of numbers is 2, 3, 4, 5, 6, 8, 10 or 12.


    With the sum of  2, there is  1 pair,   (1,1).

    With the sum of  3, there are 2 pairs.  (1,2) and (2,1).

    With the sum of  4, there are 3 pairs.  (1,3), (2,2), (3,1).

    With the sum of  5, there are 4 pairs.

    With the sum of  6, there are 5 pairs.

    With the sum of  8, there are 5 pairs.

    With the sum of 10, there are 3 pairs.

    With the sum of 12, there is  1 pair.


In total, there are  1 + 2 + 3 + 4 + 5 + 5 + 3 + 1 = 24 favorable pairs.


So the probability is  p = {{{24/36}}} = {{{2/3}}}.
&lt;/pre&gt;

Solved.


Solve the other part of the problem in a similar way. 


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If you want to learn nore about this subject and this class of problems, &amp;nbsp;look into the lesson

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Rolling-a-pair-of-fair-dice.lesson&gt;Rolling a pair of fair dice&lt;/A&gt; 

in this site. &amp;nbsp;You will find there many similar solved problems.



Also, &amp;nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson&gt;ALGEBRA-II - YOUR ONLINE TEXTBOOK&lt;/A&gt;.


The referred lesson is the part of this online textbook under the topic &amp;nbsp;&quot;&lt;U&gt;Solved problems on Probability&lt;/U&gt;&quot;. 



Save the link to this textbook together with its description


Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson


into your archive and use when it is needed.



</PRE>