.
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.
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
The lessons to learn from my post are THESE :
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).
Solved and completed.
------------------------
To see other similar solved problems on rolling dice, look into the lesson
- Rolling a pair of fair dice
in this site.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic "Solved problems on Probability".
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.