Question 1139354
.


Although the problem includes MANY question, it is SIMPLE due to its nature.

Nevertheless, there are some useful things to learn while solving this problem,
and I am going to teach you to these useful things.


There are three such things: one is on how to organize your data in the solution;
the other is on how to organize you thoughts; and the third is how to present the solution itself.


The method and the way on  how to do it is to create an appropriate table.
I created this table below for you.


<pre>
        T   A   B   L   E 
        

blue   red   two-digit   two-digit      two-digit           two-digit        perfect square
die    die    number    numbers > 30   number div.by 11    prime numbers     or div. by 7
                            (i)           (ii)                (iii)            (c)

 1      1      11                          *                    *
 1      2      12            
 1      3      13                                               *
 1      4      14                                                               *
 1      5      15
 1      6      16                                                               *

 2      1      21                                                               *
 2      2      22                          *
 2      3      23                                               *
 2      4      24
 2      5      25                                                               *
 2      6      26

 3      1      31           *                                   *
 3      2      32           *
 3      3      33           *              *
 3      4      34           *
 3      5      35           *                                                   *
 3      6      36           *                                                   *

 4      1      41           *                                   *
 4      2      42           *                                                   *
 4      3      43           *                                   *
 4      4      44           *              *
 4      5      45           *
 4      6      46           *
    
 5      1      51           *
 5      2      52           *
 5      3      53           *                                   *
 5      4      54           *
 5      5      55           *              *
 5      6      56           *                                                   *

 6      1      61           *                                   *
 6      2      62           *
 6      3      63           *                                                   *
 6      4      64           *                                                   *
 6      5      65           *
 6      6      66           *              *


the number of            4*6 = 24          6                    8              10
favored outcomes

the probability          24/36=2/3      6/36=1/6             8/36=2/9        10/36 = 5/18
under the question
</pre>


The lessons to learn from my post are <U>THESE</U> :


<pre>
    When you organize your data by a reasonable way, it may help you to save your time and efforts while solving a problem;

    It may prevent you of doing repeating operations;

    It provides you the way to present your solution to others and educate yourself and others (yours pupils).
</pre>

Solved and completed.


------------------------


To see other similar solved problems on rolling dice, 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.


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.