Question 1163422
.


Part   (i)


<pre>
The sample space is the set of all pairs (a,b), where "a" and "b" are integer numbers from 1 to 6 inclusive,
representing possible outcomes tossing of two dice.


So, the sample space has 6*6 = 36 elements, and they all have the same probability of  {{{1/36}}}  each.


Now let's calculate the number of events with the odd sum of outcomes.


    2 elements have the sum 3 :  (1,2) and (2,1).

    4 elements have the sum 5 :  (1,4), (2,3), (3,2) and (4,1).

    6 elements have the sum 7 :  (1,6), (2,5), (3,4), (4,3), (5,2) and (6,1)

    4 elements have the sum 9 :  (3,6), (4,5), (6,3) and (5,4)

    2 elements have the sum 11:  (5,6) and (6,5).


The total number of events with the odd sum is  2 + 4 + 6 + 4 + 2 = 18.


Of them, the number of events with the sum 7 is 6.


Therefore, the conditional probability under the problem's question is  {{{P(7)/P(odd)}}} = {{{((6/36))/((18/36))}}} = {{{6/18}}} = {{{1/3}}}.    <A>ANSWER</U>
</pre>


Part (ii).  &nbsp;&nbsp;Do this part similarly.




Part &nbsp;&nbsp;(iii) &nbsp;is a good entertainment problem.


Its destination is to solve the problem &nbsp;MENTALLY &nbsp;and &nbsp;MOMENTARILY &nbsp;and to make a reader laughing.


The answer is: &nbsp;&nbsp;the probability is zero, &nbsp;since the number &nbsp;7 &nbsp;is not the sum of two equal integer numbers.



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If you want to learn this subject and this class of problems &nbsp;BETTER, &nbsp;DEEPER &nbsp;and &nbsp;WIDER, &nbsp;look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Rolling-a-pair-of-fair-dice.lesson>Rolling a pair of fair dice</A> 

in this site. &nbsp;You will find there many other similar solved problems.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook under the topic &nbsp;"<U>Solved problems on Probability</U>". 



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.